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Results tagged with gn.general-topology
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user 4903
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
11
votes
3
answers
1k
views
Can there be two continuous real-valued functions such that at least one has rational values...
Of course, no continuous real valued non-constant function can attain only rational or irrational values, but can there be a pair of nowhere-constant continuous functions f and g such that for all x, …
- 656
7
votes
4
answers
2k
views
Must a linearly ordered, separable space be metrizable?
Let $X$ be a linearly ordered topological space with a countable dense subset. Does it necessarily follow that $X$ is metrizable?
EDIT: Apollo's comment int he answers implies the answer is negative. …
- 656
6
votes
3
answers
739
views
Characterization of Tychonoff spaces in terms of open sets
Metrizability and complete regularity are topological properties that are, in a sense, different from the Hausdorff condition because they are not defined purely in the terms of the open sets, but rat …
- 656