General topology: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2020]
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Unbekannt Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 313-314 |
| Physical Description: | XI, 314 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm x 17 cm |
| ISBN: | 9783110686562 3110686562 |
Staff View
MARC
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| 245 | 1 | 0 | |a General topology |b an introduction |c Tom Richmond |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XI, 314 Seiten |b Illustrationen, Diagramme (teilweise farbig) |c 24 cm x 17 cm | ||
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Record in the Search Index
| _version_ | 1804181891247505408 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
0
PRELIMINARIES
*
1
0.1
REAL
NUMBERS
*
1
0.2
SETS
------
2
0.3
QUANTIFIERS
AND
LOGIC
*
4
0.4
FUNCTIONS
------
6
0.5
COUNTABLE
AND
UNCOUNTABLE
SETS
*
7
0.6
EQUIVALENCE
RELATIONS
AND
PARTITIONS
*
10
0.7
PARTIAL
ORDERS
*
12
1
TOPOLOGIES
*
21
1.1
THE
EUCLIDEAN
METRIC
*
21
1.2
OPEN
SETS
IN
METRIC
SPACES
*
27
1.3
TOPOLOGIES
-----
31
1.4
BASIS
FOR
A
TOPOLOGY
-----
39
1.4.1
NEIGHBORHOOD
BASES
*
47
1.5
CLOSURE
AND
INTERIOR
-----
52
1.5.1
BOUNDARY
POINTS
-----
56
1.6
LIMIT
POINTS
-----
61
2
NEW
TOPOLOGIES
FROM
EXISTING
TOPOLOGIES
*
65
2.1
SUBSPACES
-----
65
2.2
FINITE
PRODUCTS
OF
SPACES
-----
69
2.3
QUOTIENT
SPACES
*
75
3
CONTINUITY-----
85
3.1
CONTINUITY
-----
85
3.2
SPECIAL
CONTINUOUS
FUNCTIONS
*
93
3.2.1
HOMEOMORPHISMS
-----
93
3.2.2
PROJECTION
FUNCTIONS
-----
98
3.2.3
COORDINATE
FUNCTIONS
*
99
4
CONNECTEDNESS
*
103
4.1
CONNECTEDNESS
*
103
4.2
PATH
CONNECTEDNESS
*
109
5
COMPACTNESS
*
115
5.1
COMPACTNESS
-----
115
5.2
COMPACTNESS
IN
METRIC
SPACES
*
124
X
*
*
CONTENTS
6
METRIC
SPACES
AND
REAL
ANALYSIS
*
133
6.1
METRIC
SPACES
-----
133
6.2
INFINITE
PRODUCTS
AND
FUNCTIONAL
ANALYSIS
*
143
6.3
THE
COCOUNTABLE
TOPOLOGY
*
153
7
SEPARATION
AXIOMS
AND
COMPACTIFICATIONS
*
157
7.1
SEPARATION
AXIOMS
*
157
7.2
SEPARATION
BY
CONTINUOUS
FUNCTIONS
*
163
7.3
COMPACTIFICATIONS
*
167
7.4
PROOF
OF
THE
TYCHONOFF
THEOREM
*
176
8
ALEXANDROFF
SPACES
*
181
8.1
ALEXANDROFF
TOPOLOGIES
*
182
8.2
QUASIORDERS
-----
188
8.3
ALEXANDROFF
TOPOLOGIES
AS
QUASIORDERS
*
194
9
LATTICE
PROPERTIES
*
201
9.1
LATTICE
THEORY
*
201
9.2
COMPACT
AND
HAUSDORFF
TOPOLOGIES
IN
T(X)
*
207
9.3
SUBLATTICES
AND
COMPLEMENTS
IN
T(X)
*
213
10
PARTIALLY
ORDERED
TOPOLOGICAL
SPACES
*
219
10.1
PARTIALLY
ORDERED
TOPOLOGICAL
SPACES
*
219
10.2
NORMALLY
ORDERED
TOPOLOGICAL
SPACES
*
226
11
VARIATIONS
ON
METRIC
SPACES
*
233
11.1
PSEUDOMETRICS
*
233
11.2
QUASI-METRICS
*
238
11.3
PARTIAL
METRICS
*
245
11.4
OTHER
VARIATIONS
OF
METRICS
*
249
12
UNIFORM
STRUCTURES
*
253
12.1
UNIFORM
CONTINUITY
IN
METRIC
SPACES
*
253
12.2
UNIFORMITIES
-----
258
12.2.1
RELATIONS
-----
259
12.2.2
FILTERS
-----
260
12.2.3
UNIFORMITIES
-----
261
12.2.4
BASE
FOR
A
UNIFORMITY
------
263
12.3
THE
UNIFORM
TOPOLOGY
------
266
12.3.1
CLOSURE
AND
INTERIOR
*
266
12.3.2
THE
SQUARE
OF
A
UNIFORM
SPACE
*
268
12.3.3
UNIFORM
CONTINUITY
-----
272
CONTENTS
*
XI
12.4
12.5
UNIFORMITIES
AND
PSEUDOMETRICS
*
274
QUASI-UNIFORMITIES
*
278
13
13.1
13.2
13.3
13.4
CONTINUOUS
DEFORMATION
OF
SETS
AND
CURVES
*
283
CONTINUOUS
DEFORMATION
OF
CLOSED
SETS
IN
IR
2
*
283
CONTINUOUS
DEFORMATION
OF
PLANAR
CURVES
*
289
THE
FUNDAMENTAL
GROUP
-----
294
THE
VIETORIS
TOPOLOGY
AND
THE
HAUSDORFF
METRIC
*
299
INDEX
*
307
BIBLIOGRAPHY
*
313
|
| adam_txt |
CONTENTS
PREFACE
*
V
0
PRELIMINARIES
*
1
0.1
REAL
NUMBERS
*
1
0.2
SETS
------
2
0.3
QUANTIFIERS
AND
LOGIC
*
4
0.4
FUNCTIONS
------
6
0.5
COUNTABLE
AND
UNCOUNTABLE
SETS
*
7
0.6
EQUIVALENCE
RELATIONS
AND
PARTITIONS
*
10
0.7
PARTIAL
ORDERS
*
12
1
TOPOLOGIES
*
21
1.1
THE
EUCLIDEAN
METRIC
*
21
1.2
OPEN
SETS
IN
METRIC
SPACES
*
27
1.3
TOPOLOGIES
-----
31
1.4
BASIS
FOR
A
TOPOLOGY
-----
39
1.4.1
NEIGHBORHOOD
BASES
*
47
1.5
CLOSURE
AND
INTERIOR
-----
52
1.5.1
BOUNDARY
POINTS
-----
56
1.6
LIMIT
POINTS
-----
61
2
NEW
TOPOLOGIES
FROM
EXISTING
TOPOLOGIES
*
65
2.1
SUBSPACES
-----
65
2.2
FINITE
PRODUCTS
OF
SPACES
-----
69
2.3
QUOTIENT
SPACES
*
75
3
CONTINUITY-----
85
3.1
CONTINUITY
-----
85
3.2
SPECIAL
CONTINUOUS
FUNCTIONS
*
93
3.2.1
HOMEOMORPHISMS
-----
93
3.2.2
PROJECTION
FUNCTIONS
-----
98
3.2.3
COORDINATE
FUNCTIONS
*
99
4
CONNECTEDNESS
*
103
4.1
CONNECTEDNESS
*
103
4.2
PATH
CONNECTEDNESS
*
109
5
COMPACTNESS
*
115
5.1
COMPACTNESS
-----
115
5.2
COMPACTNESS
IN
METRIC
SPACES
*
124
X
*
*
CONTENTS
6
METRIC
SPACES
AND
REAL
ANALYSIS
*
133
6.1
METRIC
SPACES
-----
133
6.2
INFINITE
PRODUCTS
AND
FUNCTIONAL
ANALYSIS
*
143
6.3
THE
COCOUNTABLE
TOPOLOGY
*
153
7
SEPARATION
AXIOMS
AND
COMPACTIFICATIONS
*
157
7.1
SEPARATION
AXIOMS
*
157
7.2
SEPARATION
BY
CONTINUOUS
FUNCTIONS
*
163
7.3
COMPACTIFICATIONS
*
167
7.4
PROOF
OF
THE
TYCHONOFF
THEOREM
*
176
8
ALEXANDROFF
SPACES
*
181
8.1
ALEXANDROFF
TOPOLOGIES
*
182
8.2
QUASIORDERS
-----
188
8.3
ALEXANDROFF
TOPOLOGIES
AS
QUASIORDERS
*
194
9
LATTICE
PROPERTIES
*
201
9.1
LATTICE
THEORY
*
201
9.2
COMPACT
AND
HAUSDORFF
TOPOLOGIES
IN
T(X)
*
207
9.3
SUBLATTICES
AND
COMPLEMENTS
IN
T(X)
*
213
10
PARTIALLY
ORDERED
TOPOLOGICAL
SPACES
*
219
10.1
PARTIALLY
ORDERED
TOPOLOGICAL
SPACES
*
219
10.2
NORMALLY
ORDERED
TOPOLOGICAL
SPACES
*
226
11
VARIATIONS
ON
METRIC
SPACES
*
233
11.1
PSEUDOMETRICS
*
233
11.2
QUASI-METRICS
*
238
11.3
PARTIAL
METRICS
*
245
11.4
OTHER
VARIATIONS
OF
METRICS
*
249
12
UNIFORM
STRUCTURES
*
253
12.1
UNIFORM
CONTINUITY
IN
METRIC
SPACES
*
253
12.2
UNIFORMITIES
-----
258
12.2.1
RELATIONS
-----
259
12.2.2
FILTERS
-----
260
12.2.3
UNIFORMITIES
-----
261
12.2.4
BASE
FOR
A
UNIFORMITY
------
263
12.3
THE
UNIFORM
TOPOLOGY
------
266
12.3.1
CLOSURE
AND
INTERIOR
*
266
12.3.2
THE
SQUARE
OF
A
UNIFORM
SPACE
*
268
12.3.3
UNIFORM
CONTINUITY
-----
272
CONTENTS
*
XI
12.4
12.5
UNIFORMITIES
AND
PSEUDOMETRICS
*
274
QUASI-UNIFORMITIES
*
278
13
13.1
13.2
13.3
13.4
CONTINUOUS
DEFORMATION
OF
SETS
AND
CURVES
*
283
CONTINUOUS
DEFORMATION
OF
CLOSED
SETS
IN
IR
2
*
283
CONTINUOUS
DEFORMATION
OF
PLANAR
CURVES
*
289
THE
FUNDAMENTAL
GROUP
-----
294
THE
VIETORIS
TOPOLOGY
AND
THE
HAUSDORFF
METRIC
*
299
INDEX
*
307
BIBLIOGRAPHY
*
313 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Richmond, Tom |
| author_GND | (DE-588)1213911486 |
| author_facet | Richmond, Tom |
| author_role | aut |
| author_sort | Richmond, Tom |
| author_variant | t r tr |
| building | Verbundindex |
| bvnumber | BV046967732 |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)1194976811 (DE-599)DNB1206052295 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV046967732 |
| illustrated | Illustrated |
| index_date | 2024-07-03T15:46:14Z |
| indexdate | 2024-07-10T08:58:51Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110686562 3110686562 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032375962 |
| oclc_num | 1194976811 |
| open_access_boolean | |
| owner | DE-83 DE-20 DE-703 DE-11 |
| owner_facet | DE-83 DE-20 DE-703 DE-11 |
| physical | XI, 314 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm x 17 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Richmond, Tom Verfasser (DE-588)1213911486 aut General topology an introduction Tom Richmond Berlin ; Boston De Gruyter [2020] © 2020 XI, 314 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Literaturverzeichnis: Seite 313-314 Topologie (DE-588)4060425-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Topologie (DE-588)4060425-1 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-068672-2 Erscheint auch als Online-Ausgabe, PDF 978-3-11-068657-9 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110686562&searchTitles=true 2020-03-11 Verlag Unbekannt V:DE-605;X:Imageware application/pdf http://digitale-objekte.hbz-nrw.de/storage2/2020/09/25/file_23/8919302.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032375962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Richmond, Tom General topology an introduction Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4151278-9 |
| title | General topology an introduction |
| title_auth | General topology an introduction |
| title_exact_search | General topology an introduction |
| title_exact_search_txtP | General topology an introduction |
| title_full | General topology an introduction Tom Richmond |
| title_fullStr | General topology an introduction Tom Richmond |
| title_full_unstemmed | General topology an introduction Tom Richmond |
| title_short | General topology |
| title_sort | general topology an introduction |
| title_sub | an introduction |
| topic | Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topologie Einführung |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110686562&searchTitles=true http://digitale-objekte.hbz-nrw.de/storage2/2020/09/25/file_23/8919302.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032375962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT richmondtom generaltopologyanintroduction AT walterdegruytergmbhcokg generaltopologyanintroduction |
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