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Results tagged with gn.general-topology
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user 365252
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
9
votes
1
answer
290
views
Connected open sets in the topology generated by the collection of connected open sets
Let $(X,\mathcal{T})$ be a connected topological space. Let $\mathcal{T}'$ be the topology on $X$ that is generated by the collection of connected open sets in $(X,\mathcal{T})$. That is, the connecte …
2
votes
1
answer
282
views
A characterization of continuity in terms of preservation of connected sets. Where to find t...
There is a result that if $X$ is a locally connected space and $Y$ is a locally compact Hausdorff space, then a function $f \colon X \to Y$ is continuous if and only if $f$ has a closed graph and for …
2
votes
0
answers
83
views
Union of two open, open-unicoherent sets whose intersection is connected
I stumbled upon the following proposition, and haven't found an error in my proof yet.
By "open-unicoherence" I mean unicoherence with closed sets replaced with open sets in the definition.
Let $X$ b …