Hapësirat metrike: = Metric spaces
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| Format: | Book |
| Language: | Albanian |
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Prishtinë
Akademia e Shkencave dhe e Arteve e Kosovës
2014
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| Series: | Botime të veçanta. Seksioni i shkencave të natyrës
Libri 22 |
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| Online Access: | Inhaltsverzeichnis Literaturverzeichnis Register // Sachregister |
| Physical Description: | xiii, 342 Seiten |
| ISBN: | 9789951615297 |
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| 245 | 1 | 0 | |a Hapësirat metrike |b = Metric spaces |c Qamil Haxhibeqiri |
| 246 | 1 | 1 | |a Metric spaces |
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| adam_text | Pérmbajtja
Parathénie........................................vii
1 KUPTIMII HAPÉSIRÉS METRIKE.......................1
i.iPérkufizimi i largsesés dhe i hapésirés metrike. Shembuj.1
i.2Hapèsirat e normuara dhe ato unitare............15
1.3 Detyra....................................... 18
2 VEPRIMET ME HAPÈSIRA METRIKE....................25
2.1 Nénhapésira e hapésirés metrike................25
2.2 Prodhimi i hapésirave metrike..................27
2.3 Detyra...................................... 32
3 DISAKUPTIME METRIKE.............................35
3.1 Bashkésité e kufizuara.........................35
3.2 Bashkésité plotésisht té kufizuara.............41
3.3 Detyra.........................................46
4 DISA KUPTIME TOPOLOGJIKE........................53
4.1 Bashkésité e hapura............................53
4.2 Mbyllja dhe kufiri i bashkésisé. Bashkésité e mbyllura..61
4.3 Hapésirat separabile. Baza e hapésirés.........71
4.4 Metrika e Hausdorfit...........................75
4.5 Detyra.........................................79
5 KLASÈ TE NDRYSHME TÈ FUNKSIONEVE................87
5.1 Funksionet e vazhdueshme.......................87
5.2 Funksionet uniformisht té vazhdueshme..........94
5.3 Disa veti té hapésirave metrike...............105
5.4 Metrikát ekuivalente..........................107
5.5 Detyra........................................110
6 KONVERGJENCA...................................121
6.1 Konvergjenca e vargjeve né hapésirat metrike..121
6.2 Nénvargjet dhe konvergjenca...................127
6.3 Konvergjenca e vargjeve funksionale...........131
6.4 Detyra........................................136
vi
7 HAPÉSIRAT E PLOTA METRIKE.........................141
7.1 Vargjet e Koshit dhe disa veti té tyre...........141
7.2 Hapésirat e plota metrike........................145
7.3 Teorema e Banahut mbi pikén fikse................151
7.4 Zbatime té teoremés sé Banahut mbi pikén fikse...156
Zbatime né analizén reale.........................156
Zbatime né algjebrén lineare......................158
7.5 Teorema e Kantorit...............................162
7.6 Teorema e Berit..................................165
7.7 Plotésimi i hapésirave metrike...................169
7.8 Detyra...........................................174
8 KOMPAKTÉSIA.......................................179
8.1 Pérkufizimi dhe disa veti té hapésirave kompakte.179
8.2 Funksionet e vazhdueshme né bashkésité kompakte....182
8.3 Disa kritere mbi kompaktésiné e hapésirave metrike.185
8.4 Prodhimi metrik i hapésirave kompakte............189
8.5 Kompaktésia relative. Teorema e Arcela-Askolit...191
8.6 Detyra...........................................194
9 LIDHSHMÉRIA.......................................199
9.1 Hapésirat e lidhura..............................199
9.2 Komponentet e lidhshmérisé.......................207
9.3 Hapésirat e lidhura sipas rrugéve................210
9.4 Komponentet e lidhshmérisé sipas rrugéve.........212
9.5 Detyra...........................................213
10 ZGJIDHJET E DETYRAVE DHE UDHÉZIMET.................219
Summary................................................331
Literatura.............................................337
Indeksi
339
Literatura
[1] Adamson, I.A., A General Topology Workbook, Birkhauser, Boston, 1996.
[2] Bredon, G.E., Topology and Geometry, Springer-Verlag,New York,Inc., 1993.
[3] Brown, R., Topology: A Geometric Account of General Topology, Homo-
topy Types and the Fundamental Groupoid, Ellis Horwood Limited, New
York,1988.
[4] Buskes, G.,van Rooij, A., Topological Spaces, From Distance to Neighborhood,
Springer-Verlag, New York,Inc., 1997.
[5] Copson, E.T., Metric Spaces, Cambridge University Press, Cambridge, 1968.
[6] Čerin, Z., Metrički prostori, botim interneti, Zagreb,2007.
[7] Dugundji, J., Topology, Allyn and Bacon, Boston, 1972
[8] Engelking,R., General Topology, PWN, Warszawa, 1977.
[9] Engelking,R., Siekhicki, K., Geometria i topologia, Czesć II, Topologia,
PWN, Warszawa, 1980.
[10] Gazidede, B., Analiza matematike 1, Tirane, 2006.
[11] Giles, J.R., Introduction to the Analysis of Metric Spaces, Cambridge Univer-
sity Press, Cambridge, 1987.
[12] Haxhibeqiri, Q., Topologjia, ETMM, Prishtine, 1989.
[13] Haxhibeqiri, Q., Permbledhje detyrash nga topologjia, Universiteti i Pr-
ishtiness, Prishtine, 1996.
[14] Hocking, J.G., Young, G.S., Topology,Addison-^Wesley PublishingCom-
pany,Inc.,Reading,Mass., 1961
[15] Kolmogorov, A.N., Fomin, S.V., Elementi teorii funkcij i funkcionalnovo
analiza,”Nauka”, Moskva, 1989.
[16] Kumaresan, S., Topology of Metric Spaces, Alpha Science International, Ltd.
Harrow, U.K., 2005.
[17] Kuratowski, K., Wstep do teorii mnogosci i topologii, PWN, Warszawa, 1980.
337
338
LITERATURA
[18] Mardešić, S., Matematička Analiza I, Školska knjiga, Zagreb, 1974.
[19] Marjanović,M., Metrički prostori, Stiltjesov i Lebesgueov integral, Naučna
knjiga, Beograd 1968.
[20] MarjanovićM., Vrećica, S., Topologija, Beograd, 2011.
[21] Messer, R., Straffin, P., Topology Now!, The Mathematical Association of
America, 2006.
[22] Minga,A., Kurs i algjebrs se larte, Tirane, 1972.
[23] Morris, S.A., Topology without tears, botim interneti, 2012.
[24] Mršević, M., Zbirka rešenih zadataka iz topologije, Naučna knjiga, Beograd,
1982.
[25] Munkres,J.R., Topology, Prentice Hall,New-York,2000.
[26] N.O., E.D., Opšta topologija, botim interneti, Tuzla, 2008.
[27] Searcoid,M.O., Metne Spaces,Springer, London, 2007.
[28] Sieklucki, K., Geometria i topologia, Cześć I, Geometria, PWN, Warszawa,
1979.
[29] Sieradski,A.J., An Introduction to Topology and Homotopy, PWS-KENT
Publishing Company, Boston, 1992.
[30] Steen, L.A., Seebach, J.,Jr., Counterexamples in Topology, Dover Publica-
tions,INc., New York, 1995.
[31] Sutherland, W.A., Introduction to metric and topological spaces, Claredon
Press, Oxford, 1975.
[32] Ungar, Š., Matematička analiza III, botim interneti, Zagreb, 2002.
[33] Ungar, Š., Matematička analiza IV, botim interneti, Zagreb, 2005.
[34] Viro, O.Y., Ivanov, O.A., Netsvetaev, N.Y., Kharlamov,V.M., Elementary
Topology, A first Course - Textbook in Problems, botim interneti, 2005.
[35] Yan, M., Topology, botim interneti, 2002.
indeksi
i hapesires X, 214
Diametri
i bashkésisé, 38
i hapésirés, 30
Drejtéza
euklidiane, 9
reale, 9
reale (euklidiane), 59
Aksioma
e dyte e numerueshmerise, 73
Bashkesi
te ndashme, 85
Bashkesia
FH, 120
FM , 119
derivat, 62
e barasvazhdueshme e funksioneve,
192
e hapur (e hapesires metrike), 53
e hapur (e hapesires topologjike), 58
e kategorise se dyte, 167
e kategorise se pare, 167
e kufizuar, 38
e lidhur, 199
e lidhur sipas rrugeve, 210
e mbyllur , 62
e persosur, 62
e palidhur , 199
funksionalisht e hapur, 120
funksionalisht e mbyllur, 119
invariante (e pandryshueshme), 176
konvekse, 50
kudo e ngjeshur, 70
kudo e pangjeshur, 70, 167
plotesisht e kufizuar, 41
relativisht kompakte, 191
uniformisht e kufizuar e funksion-
eve, 192
Baza
e hapesires, 72
Brendia
e bashkesise, 53
Copetimi
Fillimi
i rrugés, 210
Funksioni
(di,(¿2) - i vazhdueshém, 87
diagonal, 103
gjysmé i vazhdueshém nga ana e poshtme,
117
gjysmé i vazhdueshém nga ana e sipérme,
117
i Dirihleut, 140
i hapur, 90
i Holderit me konstantén c dhe tregües
a, 118
i kombinuar i funksioneve f dhe /2,
91
i Lipshitsit, 97
i mbyllur, 90
i ngjashmérisé (me indeks c), 100
i pérkémbyeshém (komutativ), 176
i vazhdueshém (i hapésirave topologjike),
90
i vazhdueshém né bashkési, 87
i vazhdueshém né piké, 87
izometrik, 100
qé nuk e rrit largesén, 97
uniformisht i vazhdueshém, 94
339
340
INDEKSI
Hapésira
B(y,R), 13
C[a,b] 12
Ti„ 106
T2ì 106
m, 13
c, 13
co, 13
diskrete, 55
- Z/p, 10
e Banahut, 145
e dytè e numèrueshme, 73
e Hausdorfìt, 106
e Hilbertit, 10, 145
e kufìzuar, 38
e lidhur, 199
e lidhur sipas rrugéve, 210
e Lindelofit, 185
e normuar , 15
e palidhur (jo e lidhur) , 199
e piote metrike, 145
e rregullt , 106
e Sierpinskit, 214
euklidiane, 8
euklidiane me n - permasa, 59
finalisht kompakte, 185
kofinite, 84
kompakte, 179
kompakte sipas vargjeve, 185
metrike, 1
metrike e Sierpinskit, 22
normale,, 106
numérueshmèrisht kompakte, 185
plotèsisht e palidhur, 208
plotésisht e kufìzuar, 41
plotèsisht e rregullt, 106
pseudometrike, 2
separabile, 71
topologjike, 58
topologjike diskrete, 58
topologjike indiskrete, 58
ultrametrike, 20, 49
unitare, 17
vektoriale e normuar, 15
Hapèsirat
homeomorfe, 93
e ngjashme, 100
izometrike, 100
uniformisht homeomorfe, 100
Homeomorfizmi, 93
uniform, 100
Izometria, 100
Izomorflzmi
i plotěsimeve tě hapěsirave metrike,
169
Koeeficienti
i kontraksionit, 151
Komponenta, 207
rrugore, 212
rrugore e pikěs x, 212
tě lidhshměrisě, 207
Kontraksioni (shtypja,tkurrja), 151
Konturi
i bashkěsisě, 62
Konvergjenca
sipas pikavę e vargut funksional, 131
uniforme e vargut funksional, 131
Kubi
i Hilbertit, 26
Kufiri
i bashkěsisě, 62
Lěkundja
e fuksionit ƒ ne pike., 117
Largesa, 1
e pikěs nga bashkěsia, 44
nděrmjet pikavę, 2
ndrmjet dy bashkěsive, 44
Limiti
i vargut, 122
i zakonshěm i vargut funksional, 131
sipas pikavę i vargut funksional, 131
uniform i vargut funksional, 131
Luhatja
e funksionit ƒ ně pike, 117
Mběshtjellěsi konveks, 50
Mbarimi (fundi) i rrugěs, 210
Mbuloja, 179
INDEKSI
341
e hapur (mbyllur), 179
Mbyllja
e bashkesıse, 62
Metrika, 1
max né Rn, 9
10-adike né Z, 14
LP, 10
lp, 9
max né C[a^j, 12
sup né J5(y,R), 13
diskrete, 55
e Hausdorfit, 75
e indukuar, 25
e pércaktuar (pérftuar) me normén,
16
e pércaktuar (pérftuar) me prodhimin
nümerik (skalar), 18
e prodhimit, 31
e prodhimit (te njé numri te fundmé
hapésirash), 28
e zakonshme né Rn, 8
euklidiane né Rn, 8
kendőre, 23
postare, 22
radiale, 22
triviale (diskrete), 8
uniformé, 13
Metrikát
ekuivalente sipas Lipshitsit, 107
topologjikisht ekuivalente, 107
uniformisht ekuivalente, 107
Moduli
i vazhdueshmérisé i funksionit, 117
Nénbashkésia
kompakté, 180
Nénhapésira, 25
e hapésirés metrike, 25
e hapésirés topologjike, 60
Nénmbuloja, 179
Nénvargu, 128
Ndarja
e hapésirés X, 214
jotriviale, 214
triviale, 214
Ngjashmeria
(me indeks e), 100
Norma, 15
e percaktuar (perftuar) me prodhimin
nümerik, 17
euklidiane, 17
Numra te koniuguar, 3
Numri i Lebegut, 184
Operatori
linear i hapesirave vektorıale te nor-
muara, 112
linear i kufizuar, 112
Pabarazimi
i Holderit, 4
i Koshi - Shvarc - Bunjakovskit, 7
i Minkovskit, 6
i shumekendeshit, 2
i trekendeshit, 15
pabarazimi
i trekendeshit, 1
Pika
e brendshme, 53
e grumbullimit te bashkesıse, 62
e grumbullimit te var gut, 128
e izoluar, 62
e keputjes se funksionit ƒ, 88
e kondensimit, 81
e palevizshme e funksionit, 151
e takimit te bashkesıse, 61
fikse e funksionit, 151
limite e vargut, 122
te lidhura, 207
te lidhura me rruge, 210
Plotesimet izomorfe, 169
Plotesimi
i hapesires metrike, 169
Prodhimi
i drejtperdrejte i bashkesıse se funk-
sioneve, 115
metrik, 28, 31
nümerik (skalar) ne X, 17
Programı i Erlangenit, 101
Projeksioni
342
INDEKSI
né faktorin e ¿—té, 32
Pseudometrika, 2
konvergjent, 122
pothuajse konstant, 123
stacionar, 123
themelor, 141
uniformisht i kufizuar, 140
Retraksioni, 176
Rrafshi
euklidian, 9
projektiv, 23
real, 9
real (euklidian), 59
Vetia
e gjeometrisé sé ngjashmérive, 101
e pikés fikse, 176
e prerjes se fundme, 194
e vlerés sé ndérmjetme, 215
metrike, 101
topologjike, 101
uniforme topologjike, 101
e intervalit, 201
Rrethina
e pikés, 61
Rrotullimi, 104
Rruga, 210
Rruzulli
i hapur, 35
i mbyllur, 35
Zhvendosja
paralele, 103
Zhytja (vendosja)
diagonale, 103
Sfera, 35
simetria
ndaj boshtit Ox, 151
Teorema
e Banahut mbi pikén fikse, 152
e Kant orit, 162
mbi vier én e ndérmjetme, 202
Topologjia, 58
pérjashtuese e pikés, 84
diskrete, 58
e pikés sé veganté, 84
e pércaktuar me metrikén d, 58
e zakonshme(euklidiane) né Rn, 59
indiskrete, 58
kofinite, 84
relative, 60
Translacioni, 103
Ultrametrika, 20, 49
Vargu, 121
fundamental, 141
i Koshit, 141
i kufizuar, 124
i rruzujve qé shtréngohen, 163
i rruzujve te futur njéri brenda tjetrit,
163
konstant, 123
|
| any_adam_object | 1 |
| author | Haxhibeqiri, Qamil 1949- |
| author_GND | (DE-588)1144655277 |
| author_facet | Haxhibeqiri, Qamil 1949- |
| author_role | aut |
| author_sort | Haxhibeqiri, Qamil 1949- |
| author_variant | q h qh |
| building | Verbundindex |
| bvnumber | BV043827275 |
| ctrlnum | (OCoLC)1012424454 (DE-599)BVBBV043827275 |
| format | Book |
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| id | DE-604.BV043827275 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:36:08Z |
| institution | BVB |
| isbn | 9789951615297 |
| language | Albanian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029238136 |
| oclc_num | 1012424454 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | xiii, 342 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Akademia e Shkencave dhe e Arteve e Kosovës |
| record_format | marc |
| series | Botime të veçanta. Seksioni i shkencave të natyrës |
| series2 | Botime të veçanta / Akademia e Shkencave dhe e Arteve e Kosovës Botime të veçanta. Seksioni i shkencave të natyrës |
| spelling | Haxhibeqiri, Qamil 1949- Verfasser (DE-588)1144655277 aut Hapësirat metrike = Metric spaces Qamil Haxhibeqiri Metric spaces Prishtinë Akademia e Shkencave dhe e Arteve e Kosovës 2014 xiii, 342 Seiten txt rdacontent n rdamedia nc rdacarrier Botime të veçanta / Akademia e Shkencave dhe e Arteve e Kosovës 134 Botime të veçanta. Seksioni i shkencave të natyrës Libri 22 Zusammenfassung in englischer Sprache Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s DE-604 Akademia e Shkencave dhe e Arteve e Kosovës Botime të veçanta 134 (DE-604)BV011748946 134 Botime të veçanta. Seksioni i shkencave të natyrës Libri 22 (DE-604)BV021576880 22 Digitalisierung BSB Muenchen 19 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung BSB Muenchen 19 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Literaturverzeichnis Digitalisierung BSB Muenchen 19 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000003&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Register // Sachregister |
| spellingShingle | Haxhibeqiri, Qamil 1949- Hapësirat metrike = Metric spaces Botime të veçanta. Seksioni i shkencave të natyrës Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4169745-5 |
| title | Hapësirat metrike = Metric spaces |
| title_alt | Metric spaces |
| title_auth | Hapësirat metrike = Metric spaces |
| title_exact_search | Hapësirat metrike = Metric spaces |
| title_full | Hapësirat metrike = Metric spaces Qamil Haxhibeqiri |
| title_fullStr | Hapësirat metrike = Metric spaces Qamil Haxhibeqiri |
| title_full_unstemmed | Hapësirat metrike = Metric spaces Qamil Haxhibeqiri |
| title_short | Hapësirat metrike |
| title_sort | hapesirat metrike metric spaces |
| title_sub | = Metric spaces |
| topic | Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Metrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029238136&sequence=000003&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011748946 (DE-604)BV021576880 |
| work_keys_str_mv | AT haxhibeqiriqamil hapesiratmetrikemetricspaces AT haxhibeqiriqamil metricspaces |