# 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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### Basic Topology: Limit Points

Please see the below and let me know if my logic is not correct for this problem. Thank you. Let $A = (3,4) \cup \{5,6\}$. In the standard topology, prove the following: (a) There is a point ...
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### Morphisms of action group and continuity

Let $\mathbf{G}$ be a profinite group, $\mathbf{X}$ and $\mathbf{Y}$ two finite topological spaces with a continuous action group of $\mathbf{G}$ on them. If $\mathbf{G}$ is finite, is this true that ...
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### Compact but not measurable [closed]

Does there exist a compact subset of $\Bbb{R}^n$ (with the usual topology) which is not Lebesgue measurable?
### Show any continuous function $f: \mathbb{\bar N} \to (\mathbb{R}, \tau_c)$ is eventually constant
Show any continuous function $f:\mathbb{\bar N} \to (\mathbb{R}, \tau_c)$ is eventually constant. Preliminaries: $\tau_c = \{U \subset \mathbb{R} \mid U = \emptyset \vee U^c : \text{countable} \}$...