List questions from metric-spaces

Published on 25 Mar 2026 - 6:18

1.4k

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Prob. 4, Sec. 27, in Munkres' TOPOLOGY, 2nd ed: Any connected metric space having more than one point is uncountable

Published on 29 Mar 2026 - 4:44

495

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Infinite composition of function that has a fixed point

Published on 25 Mar 2026 - 7:15

97

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Existence of Borel cover of a metric space satisfying given properties

Published on 03 Oct 2018 - 14:42

51

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Is this a valid proof that $f_{x_0}:X \to \mathbb{R}$ is continuous.

Published on 03 Oct 2018 - 21:40

59

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Limit of a sequence in a product sequence

Published on 03 Oct 2018 - 22:05

297

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Hausdorff measure on non separable spaces

Published on 25 Mar 2026 - 7:42

1.1k

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Inequality between norms in $L^p$ and $L^q$ spaces for $p,q>1$

Published on 29 Mar 2026 - 3:35

40

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Does there exist a continuous function $f$ such that $d_{x}(x_{n},x) \leq f (d_{y}(y_{n},y))$?

Published on 25 Mar 2026 - 23:37

25

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Distance between continious maps

Published on 04 Oct 2018 - 15:04

662

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How do I show that a function is not continuous?

Published on 04 Oct 2018 - 15:46

24

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Open after being projected

Published on 25 Mar 2026 - 9:45

129

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Does Cauchy imply boundedness?

Published on 05 Oct 2018 - 2:02

160

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Condition for which $ \text{dist}(x,A) = d(x,y_0)$

Published on 05 Oct 2018 - 12:07

37

Views

Measurable function but not in space $L_{\infty}(0,1)$

Published on 05 Oct 2018 - 12:36

List Question

Does the distance map send closed sets to closed sets?

Prob. 4, Sec. 27, in Munkres' TOPOLOGY, 2nd ed: Any connected metric space having more than one point is uncountable

Infinite composition of function that has a fixed point

Existence of Borel cover of a metric space satisfying given properties

Is this a valid proof that $f_{x_0}:X \to \mathbb{R}$ is continuous.

Limit of a sequence in a product sequence

Hausdorff measure on non separable spaces

Inequality between norms in $L^p$ and $L^q$ spaces for $p,q>1$

Does there exist a continuous function $f$ such that $d_{x}(x_{n},x) \leq f (d_{y}(y_{n},y))$?

Distance between continious maps

How do I show that a function is not continuous?

Open after being projected

Does Cauchy imply boundedness?

Condition for which $ \text{dist}(x,A) = d(x,y_0)$

Measurable function but not in space $L_{\infty}(0,1)$

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