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Results tagged with gn.general-topology
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user 51164
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
Accepted
Intersection of compact sets in the compact-open topology
The answer is yes if $X$ is locally compact. Indeed, consider the topological space $X \times \mathcal{K}$ and let $V = \{(x,U) \in X \times \mathcal{K} | x \in U\}$. We claim that $V$ is open in $X \ …
- 9,491
6
votes
Which sequential colimits commute with pullbacks in the category of topological spaces?
Fiber products do commute with sequential colimits of closed embedding in CGWH, but one must remember that neither limits nor colimits in CGWH are the same as the corresponding limits and colimit in t …
- 9,491
9
votes
Accepted
Is every locally compactly generated space compactly generated?
The paper "A distinguishing example in k-spaces" by John Isbell constructs an example of a locally compact space $X$ which is not compact-Hausdorffly generated.
- 9,491