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Results tagged with gn.general-topology
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user 1384
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
9
votes
1
answer
285
views
Reference request: filter tends to filter along map
Recall that a filter on a set $X$ is a nonempty collection $\mathcal{F}$ of subsets of $X$ such that
(i) $U\subseteq V\subseteq X$ and $U\in\mathcal{F}$ implies $V\in\mathcal{F}$, and
(ii) $U,V\in\m …
- 41.4k
3
votes
1
answer
502
views
Can Tychonoff's theorem be applied to topological spaces generated by program output in ZFC?
I am confused about an issue in set theory.
Tychonoff's theorem says that "an arbitrary product of compact topological spaces is compact". We often talk of an index set $I$ and then for each $n\in I$ …
- 41.4k
29
votes
Accepted
Why are topological ideas so important in arithmetic?
Why are topological ideas so important in arithmetic? In some sense KConrad is of course spot on, but let me offer a completely different kind of answer.
Why are complex functions of one variable so …
- 41.4k
107
votes
9
answers
36k
views
solving $f(f(x))=g(x)$
This question is of course inspired by the question How to solve f(f(x))=cosx
and Joel David Hamkins' answer, which somehow gives a formal trick for solving equations of the form $f(f(x))=g(x)$ on a b …
- 41.4k