List questions from metric-spaces

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Open unit ball in $C[0,1]$

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Examples of Uniform Spaces

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Questions concerning the coarsest topology on $X \times X$ for which the metric $d : X \times X \to \mathbb{R}$ is continuous

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In the following question Which topologies they are talking about?

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Convergence of sequence of functions in metric spaces

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Why does the measure of a support $1$?

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Show that $d(x,y)=|x-2y|$ defines a metric on $\mathbb R$

Published on 16 Aug 2018 - 18:43

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Why does such $M$ exist in this proof for Skorohod representation theorem?

Published on 16 Aug 2018 - 19:25

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If $X$ has more than one element, then the norm $||f||=\sup_{x\in X}|f(x)|$ doesn't come from a inner product

Published on 16 Aug 2018 - 19:46

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Help understanding this proof that $J$ is closed

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Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?

Published on 25 Mar 2026 - 12:54

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Structure theorem for closed set in R

Published on 17 Aug 2018 - 17:12

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Implications of the Lebesgue covering lemma

Published on 29 Mar 2026 - 3:53

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Uses of Cantors intersection theorem

Published on 17 Aug 2018 - 19:29

List Question

Why do we require that a perfect set is closed?

Open unit ball in $C[0,1]$

Examples of Uniform Spaces

Questions concerning the coarsest topology on $X \times X$ for which the metric $d : X \times X \to \mathbb{R}$ is continuous

In the following question Which topologies they are talking about?

Convergence of sequence of functions in metric spaces

Why does the measure of a support $1$?

Show that $d(x,y)=|x-2y|$ defines a metric on $\mathbb R$

Why does such $M$ exist in this proof for Skorohod representation theorem?

If $X$ has more than one element, then the norm $||f||=\sup_{x\in X}|f(x)|$ doesn't come from a inner product

Help understanding this proof that $J$ is closed

Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?

Structure theorem for closed set in R

Implications of the Lebesgue covering lemma

Uses of Cantors intersection theorem

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