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Results tagged with gn.general-topology
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user 175352
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
1
answer
262
views
O. Frink's characterization of completely regular spaces
Def: Suppose X is topological space and B is a base for it. We say, that B is normal base, if following properties hold:
a. For any x∈X and A∈B, with x∈A, there exist A′∈B, such that x∉A′ and A∪A′=X.
…
0
votes
Are Hausdorff compactifications of a Tychonoff space $X$ in one-to-one correspondence with c...
I can`t fully understand, if we additionally assume that A algebra is closed under complex conjugation, by that assumption, how can we finally prove that A is he smallest closed subalgebra that contai …
2
votes
1
answer
267
views
An example of a $T_1$ space where all closed $G_\delta$ sets are zero-sets, but it isn't normal
In Engelking's General topology, in the exercises section, there is Ju. M. Smirnov's characterization of normal spaces:
A $T_1$ space is normal iff the following properties hold (both):
Every closed …