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Results tagged with gn.general-topology
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user 91656
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
8
votes
1
answer
350
views
Zero-dimensional $F$-space which is not strongly zero-dimensional
Does anyone know of an example of a (Tychonoff) $F$-space which is zero-dimensional but not strongly zero-dimensional?
By an $F$-space we mean every cozeroset is $C^*$-embedded.
By zero-dimensional …
- 11.4k
-1
votes
Is every $b$-discrete space $X$ with countable injective weight basically disconnected?
Just came across this. b-discrete is a subclass of the class of weak P-spaces aka $\omega$-discrete (that is, every countable set is closed).
It is not the case that every basically disconnected space …
- 289
12
votes
Some examples of clean topological spaces
For a Tychonoff space $X$, the rings $C(X)$ and $C(X,\mathbb{C})$ are each clean if and only if the space $X$ is strongly zero-dimensional (s.z.d). This is a result of Azarpanah, me, and most recently …
- 289