# Tagged Questions

Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness; compactness; separation axioms; bases; convergence: sequences, nets and filters; continuous functions; compactifications; function spaces; ...

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### How does homeomorphism map sets boundaries?

I'm at the end of my first course on general topology, but this topic was not well developed. I can tell that an homeomorphism preserves the quality of a point to be a boundary point for a subset of a ...
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### Comparison between various types of cell complexes

There are the following (and more) types of geometric cell complexes: 1) The geometric realization of a simplicial set 2) CW-complexes 3) The geometric realization of an abstract simplicial complex ...
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### Defining a Limit Point of A Set

Limit Point is defined as: Wolfram MathWorld: A number $x$ such that for all $\epsilon \gt 0$, there exists a member of the set $y$ different from $x$ such that $|y-x| \lt \epsilon$. Proof Wiki: ...
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### On compact space with order topology

We are familar with that for the first uncountable cardinality $\omega_1$, the topological space $[0,\omega_1]$ is compact. I find the proof for the $\omega_1$, is also for every regular cardinality. ...
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### closed set in another closed set

I'm new here and I'm hoping that maybe I could get some help with something my teacher told me. He said that it is possible to have a closed set nested within another closed set where the intersection ...
I am trying to showed that if $X$ and $Y$ are path connected then $X \coprod_f Y$ is path connected. (The adjunction space). Let $A \subset X$ , and let $f:A \to Y$ be the attaching map. (Note: ...
I was able to prove an extension of the Ham Sandwich Theorem (namely; that given any 3 integrable functions on $\mathbb{R}^3$, there exists a plane which simultaneously divides their total integrals ...