Topology from Neighbourhoods
Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x)...
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| Format: | Article |
| Language: | English |
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Sciendo
2015-12-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.1515/forma-2015-0023 |
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doaj-1ccd7b0c2d5c4bb1968f67c4082f83432021-09-05T20:45:03ZengSciendoFormalized Mathematics1426-26301898-99342015-12-0123428929610.1515/forma-2015-0023forma-2015-0023Topology from NeighbourhoodsCoghetto Roland0Rue de la Brasserie 5, 7100 La Louvière, BelgiumUsing Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x in this topology.https://doi.org/10.1515/forma-2015-002354a0503b35filtertopological spaceneighbourhoods systemidentifier: fintopo7version: 8.1.04 5.34.1256 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Coghetto Roland |
| spellingShingle |
Coghetto Roland Topology from Neighbourhoods Formalized Mathematics 54a05 03b35 filter topological space neighbourhoods system identifier: fintopo7 version: 8.1.04 5.34.1256 |
| author_facet |
Coghetto Roland |
| author_sort |
Coghetto Roland |
| title |
Topology from Neighbourhoods |
| title_short |
Topology from Neighbourhoods |
| title_full |
Topology from Neighbourhoods |
| title_fullStr |
Topology from Neighbourhoods |
| title_full_unstemmed |
Topology from Neighbourhoods |
| title_sort |
topology from neighbourhoods |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1426-2630 1898-9934 |
| publishDate |
2015-12-01 |
| description |
Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]:
If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x in this topology. |
| topic |
54a05 03b35 filter topological space neighbourhoods system identifier: fintopo7 version: 8.1.04 5.34.1256 |
| url |
https://doi.org/10.1515/forma-2015-0023 |
| work_keys_str_mv |
AT coghettoroland topologyfromneighbourhoods |
| _version_ |
1717784605172432896 |