Newbetuts

Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective. [duplicate]

Given a fiber bundle $F\to E\overset{\pi}{\to} B$ such that $F,B$ are compact, is $E$ necessarily compact?

Topology counterexamples without ordinals

A example of closed and bounded does not imply compactnesss in metric Space

Understanding the definition of a compact set

Is the integral operator $I: L^1([0,1])\to L^1([0,1]), f\mapsto (x\mapsto \int_0^x f \,\mathrm d\lambda)$ compact?

Show that a subset $Y$ of metric space $X$ is separable if there exists a sequence of points in $X$ whose closure contains $Y$

If $X$ is a compact topological space and if some sequence $\{f_n\}$ of continuous functions separates points on $X$, then $X$ is metrizable

How to show that $\Omega_{c}=\left\{x \in \mathbb R^{n}: V(x) \leq c\right\}$ is compact?

How to understand compactness? [duplicate]

Why are subsets of compact sets not compact?

Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact

Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?

Open subspaces of locally compact Hausdorff spaces are locally compact

Proving that the Union of Two Compact Sets is Compact

New posts in compactness

Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective. [duplicate]

Cardinality of a locally compact Hausdorff space without isolated points

Rationals are not locally compact and compactness

Are compact spaces characterized by "closed maps to Hausdorff spaces"?

Show that the closed unit ball $B[0,1]$ in $C[0,1]$ is not compact

If $E$ is an infinite subset of a compact set $K$, then $E$ has a limit point in $K$

Given a fiber bundle $F\to E\overset{\pi}{\to} B$ such that $F,B$ are compact, is $E$ necessarily compact?

Topology counterexamples without ordinals

A example of closed and bounded does not imply compactnesss in metric Space

Understanding the definition of a compact set

Is the integral operator $I: L^1([0,1])\to L^1([0,1]), f\mapsto (x\mapsto \int_0^x f \,\mathrm d\lambda)$ compact?

Show that a subset $Y$ of metric space $X$ is separable if there exists a sequence of points in $X$ whose closure contains $Y$

If $X$ is a compact topological space and if some sequence $\{f_n\}$ of continuous functions separates points on $X$, then $X$ is metrizable

How to show that $\Omega_{c}=\left\{x \in \mathbb R^{n}: V(x) \leq c\right\}$ is compact?

How to understand compactness? [duplicate]

Why are subsets of compact sets not compact?

Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact

Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?

Open subspaces of locally compact Hausdorff spaces are locally compact

Proving that the Union of Two Compact Sets is Compact