Topology from Neighbourhoods

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)...

Full description

Bibliographic Details
Main Author: Coghetto Roland
Format: Article
Language:English
Published: Sciendo 2015-12-01
Series:Formalized Mathematics
Subjects:
54a05
03b35
filter
topological space
neighbourhoods system
identifier: fintopo7
version: 8.1.04 5.34.1256
Online Access:https://doi.org/10.1515/forma-2015-0023
Description
Summary: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.
ISSN:1426-2630
1898-9934

Similar Items