New posts in compactness

Graph of continuous function from compact space is compact.

real-analysis general-topology continuity compactness

Compactness and Strictly Finer Topologies.

general-topology compactness separation-axioms

If $A$ is compact, is then $f(A)$ compact?

real-analysis compactness

Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact

real-analysis functional-analysis compactness

Prob. 5, Sec. 27 in Munkres' TOPOLOGY, 2nd ed: Every compact Hausdorff space is a Baire space

general-topology compactness solution-verification baire-category

Extending open maps to Stone-Čech compactifications

general-topology compactness open-map compactification

Stone-Čech compactification. A completely regular topological space is locally compact iff it is open in its Stone-Čech compactification.

general-topology functional-analysis compactness

Quotient of compact metric space is metrizable (when Hausdorff)?

general-topology metric-spaces compactness quotient-spaces

Covering a compact set with balls whose centers do not belong to other balls.

real-analysis general-topology measure-theory compactness

Weak Hausdorff space not KC

general-topology compactness examples-counterexamples

Show the given space is uncountable.

general-topology compactness

What can we say about a locally compact Hausdorff space whose every open subset is sigma compact?

general-topology compactness

Compactness in subspaces

general-topology compactness

If the graph of a function $f: A \rightarrow \mathbb R$ is compact, is $f$ continuous where $A$ is a compact metric space?

real-analysis general-topology compactness

Is an expanding map on a compact metric space continuous?

general-topology metric-spaces continuity compactness

Proofs of the Riesz–Markov–Kakutani representation theorem

functional-analysis measure-theory reference-request compactness riesz-representation-theorem

Is $\mathbb{R}^n$ properly homotopy equivalent to $\mathbb{R}^m$ if $n \neq m$?

algebraic-topology compactness homotopy-theory

The smallest compactification

general-topology compactness

Compact space and Hausdorff space

general-topology compactness

An example of a compact topological space which is not the continuous image of a compact Hausdorff space?

general-topology compactness