List questions from supremum-and-infimum

Published on 26 Mar 2026 - 21:07

435

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Is it true that $d(\inf E,\sup E)=\sup\{d(x,y): x, y\in E\}$?

Published on 05 Mar 2017 - 10:58

49

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If, for every $n$, $f_n\to0$ at infinity and $|f_n(x_n)|\geq C$, can one deduce that $(x_n)$ is bounded?

Published on 29 Mar 2026 - 19:14

51

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If each $f_n$ is radial Schwartz, and $\|f_n\|_{L^{\infty}} \geq 1,$ can we choose $\{x_n\}$ bounded with $|f_n(x_n)|\geq 1$?

Published on 26 Mar 2026 - 10:43

310

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Supremum over a compact set

Published on 07 Mar 2017 - 11:05

43

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Prove that the l.u.b of A is an element of A if A is closed.

Published on 08 Mar 2017 - 9:59

464

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$X$ is bounded iff $\sup(X)$ and $\inf(X)$ are finite ($X\subseteq\mathbb{R}, X\neq\emptyset$)

Published on 08 Mar 2017 - 21:10

529

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How to show, that the set of density functions with compact support is compact wrt. Wasserstein Metric?

Published on 23 Feb 2026 - 12:14

857

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Find the supremum $(0,1)\setminus \mathbb{Q}$.

Published on 14 Mar 2017 - 0:59

34

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Supremum and Limit superior

Published on 29 Mar 2026 - 19:09

262

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the proof of the supremum of the continuity function

Published on 16 Mar 2017 - 3:07

107

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Infimum of a proper subset contained in a set with a lower bound.

Published on 16 Mar 2017 - 5:28

72

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Does the Least Upper Bound and the Greatest Lower Bound Properties implied to each others?

Published on 16 Mar 2017 - 18:43

286

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Verification of proof concerning the supremum of a set.

Published on 18 Mar 2017 - 10:00

26

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Determining a bound on the rationals in abstract algerbra.

Published on 19 Mar 2017 - 21:58

List Question

Absolute Convergence and Supremum?

Is it true that $d(\inf E,\sup E)=\sup\{d(x,y): x, y\in E\}$?

If, for every $n$, $f_n\to0$ at infinity and $|f_n(x_n)|\geq C$, can one deduce that $(x_n)$ is bounded?

If each $f_n$ is radial Schwartz, and $\|f_n\|_{L^{\infty}} \geq 1,$ can we choose $\{x_n\}$ bounded with $|f_n(x_n)|\geq 1$?

Supremum over a compact set

Prove that the l.u.b of A is an element of A if A is closed.

$X$ is bounded iff $\sup(X)$ and $\inf(X)$ are finite ($X\subseteq\mathbb{R}, X\neq\emptyset$)

How to show, that the set of density functions with compact support is compact wrt. Wasserstein Metric?

Find the supremum $(0,1)\setminus \mathbb{Q}$.

Supremum and Limit superior

the proof of the supremum of the continuity function

Infimum of a proper subset contained in a set with a lower bound.

Does the Least Upper Bound and the Greatest Lower Bound Properties implied to each others?

Verification of proof concerning the supremum of a set.

Determining a bound on the rationals in abstract algerbra.

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