New posts in second-countable

Every locally compact, second countable Hausdorff space has a countable basis of open sets with compact closure

general-topology second-countable

Lindelöf and second countable spaces

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

Compact metric spaces is second countable and axiom of countable choice

general-topology set-theory compactness axiom-of-choice second-countable

Are countable topological spaces second-countable?

general-topology second-countable

Compact topological space not having Countable Basis?

general-topology compactness examples-counterexamples product-space second-countable

Equivalence of three properties of a metric space.

general-topology metric-spaces second-countable separable-spaces

Separable implies second countable

general-topology separable-spaces second-countable

Second Countable, First Countable, and Separable Spaces

general-topology separable-spaces second-countable first-countable

If X is second-countable, then X is Lindelöf.

general-topology proof-explanation second-countable

Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?

general-topology set-theory axiom-of-choice second-countable

Show that the Sorgenfrey line does not have a countable basis.

general-topology second-countable sorgenfrey-line

A metric space is separable iff it is second countable [closed]

general-topology metric-spaces second-countable separable-spaces

Constraining a dense sequence on a product space, one factor at a time

general-topology product-space second-countable separable-spaces first-countable

cardinality of the Borel $\sigma$-algebra of a second countable space

general-topology measure-theory second-countable

Show that every compact metrizable space has a countable basis

general-topology proof-verification metric-spaces compactness second-countable

Second-countable implies separable/Axiom countable choice

general-topology elementary-set-theory axiom-of-choice separable-spaces second-countable

Hausdorff locally compact and second countable is $\sigma$-compact

general-topology second-countable

Topology counterexamples without ordinals

sequences-and-series general-topology compactness second-countable first-countable

When is $C_0(X)$ separable?

general-topology functional-analysis separation-axioms second-countable separable-spaces

On showing that every separable metric space has a countable base

real-analysis general-topology metric-spaces separable-spaces second-countable