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Second Countability Preserved under CLOSED Continuous Surjection

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#general-topology #second-countable
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An uncountable set in a second countable space has limit points.

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#general-topology #second-countable
59
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Are first and second countability preserved under intersection of topologies?

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#general-topology #second-countable #first-countable
52
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How many second-countable $T_1$ spaces are there?

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#general-topology #cardinals #separation-axioms #second-countable
51
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Prove that $S^2$ has a countable basis $\{U_n\}$ implies that $P^2$ has a countable basis $\{p(U_n)\}$.

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#general-topology #quotient-spaces #second-countable
73
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Arbitrary union of measure $0$ open sets has measure $0$ in a separable metric space

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#real-analysis #general-topology #measure-theory #borel-measures #second-countable
170
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Quotient topology, product topology and subspace topology

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#general-topology #quotient-spaces #second-countable
295
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Locally compact 2nd countable Hausdorff space and complete metrizability

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#general-topology #metric-spaces #compactness #complete-spaces #second-countable
39
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Prove that the following properties are all finitely productive

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#general-topology #solution-verification #second-countable #first-countable
25
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For non second-countable TVS, is the sum of measurable functions again measurable?

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#measure-theory #topological-vector-spaces #measurable-functions #borel-sets #second-countable
183
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Why is a Countable Basis Needed in This Proof?

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#general-topology #solution-verification #separation-axioms #second-countable
45
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Is every second countable locally compact Hausdorff space normal?

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#general-topology #second-countable
151
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Does there exist a second-countable locally connected space with no countable basis of connected sets?

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#general-topology #connectedness #second-countable
56
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Support of function

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#real-analysis #functional-analysis #second-countable #support-function
72
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If a topological space X is not first countable, is it second countable?

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#general-topology #second-countable #first-countable

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