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When is $C_0(X)$ separable?

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#general-topology #functional-analysis #separation-axioms #second-countable #separable-spaces
2.1k
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Compact metrizable space has a countable basis (Munkres Topology)

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#general-topology #metric-spaces #compactness #second-countable
3.6k
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Every $T_3$ space with a countable basis is $T_4$.

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#general-topology #separation-axioms #second-countable
5.7k
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Second-countable implies separable/Axiom countable choice

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#general-topology #elementary-set-theory #axiom-of-choice #separable-spaces #second-countable
345
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Second countability of compact open topology

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#general-topology #second-countable
717
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Manifold has a countable cover by compact sets.

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#general-topology #manifolds #second-countable
127
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Second countable space implies numerable subbasis

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#general-topology #second-countable
96
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Examples of topologies in which all open sets are countable union of base elements, but the topology itself doesn't have countable bases.

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#general-topology #second-countable #sorgenfrey-line
60
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Is this topology separable, first countable, second countable?

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#general-topology #separable-spaces #second-countable #first-countable
158
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Let X be a topological space. a) If X is Hausdorff and it has an countable base, so X is normal?

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#general-topology #separable-spaces #second-countable #first-countable
37
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Second countable space $\implies [x_n\to a, f(x_n)\to L \implies \lim\limits_{x\to a}f(x)=L]$

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#general-topology #limits #second-countable
285
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Does second countable implies countably many components?

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#general-topology #separable-spaces #second-countable
89
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Counter example in topology

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#general-topology #second-countable
399
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Is the countable union of second countable open subspaces second countable?

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#general-topology #second-countable
93
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Help me visualize a Lindelöf space and a corresponding theorem

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#real-analysis #general-topology #metric-spaces #second-countable #lindelof-spaces

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