On biradial topological spaces and groups
A space X is called biradial if for every filter base \(\xi\) converging to \(x\in X\) there exists a chain \(\eta\) converging to x and meshing with \(\xi\) (i.e. for every \(A\in \eta\) and every \(B\in \xi\), \(A\cap B\neq \emptyset)\). The main attention of the paper is given to biradial topological groups. It is proved that: 1) If X is a regular biradial space, then for every \(x\in X\) there exists a chain \(\eta\) in X consisting of open sets and converging to x. 2) A topological group G is biradial iff there exists a chain \(\eta\) consisting of open sets which is a base for the space G at the point \(e\in G\). 3) A topological group G is metrizable iff G is biradial and the pseudocharacter of G is countable.
scientific article; zbMATH DE number 4161006
scientific article