Question

For metric space $(X, d)$ and fixed $a\in X$, prove function from induced topology to $\Bbb R$ defined by $f(x) = d(a, x)$ is continuous.

score 34 · Answer 1 · 2026-04-02 05:23:42

34

Views

For metric space $(X, d)$ and fixed $a\in X$, prove function from induced topology to $\Bbb R$ defined by $f(x) = d(a, x)$ is continuous.

Published on 02 Apr 2026 - 5:23

score 82 · Answer 2 · 2026-03-27 23:38:14

82

Views

Differential Equations Proof for Equilibrium

Published on 27 Mar 2026 - 23:38

score 49 · Answer 3 · 2026-03-25 11:11:56

49

Views

Is there a name for a "continuous space of sequences"?

Published on 25 Mar 2026 - 11:11

score 58 · Answer 4 · 2018-08-05 16:29:39

58

Views

Linear transformation in space of infinite dimension

Published on 05 Aug 2018 - 16:29

score 74 · Answer 5 · 2026-02-23 01:23:46

74

Views

$M$ equicontinuous and closed set of $C([a,b],\mathbb{R})$. There is $m \geq 0$ such that $|f(a)| \leq m$ $\forall f$. Prove that $M$ is compact

Published on 23 Feb 2026 - 1:23

score 2.6k · Answer 6 · 2018-08-06 00:02:55

2.6k

Views

How to compute $\lim_{x \to 0} \frac{1}{x^2} \int_{0}^{x} f(t)t \space dt $?

Published on 06 Aug 2018 - 0:02

score 193 · Answer 7 · 2018-08-06 02:40:11

193

Views

Show that there exists no $f_0\in X$ such that $||f_0||=1$ and $\text{dist}(f_0,Y)=1$

Published on 06 Aug 2018 - 2:40

score 137 · Answer 8 · 2018-08-06 08:48:35

137

Views

Continuity and differentiability at (0,0)

Published on 06 Aug 2018 - 8:48

score 57 · Answer 9 · 2026-03-29 02:36:09

57

Views

$C(K, K)$ equipped with certain topology compact?

Published on 29 Mar 2026 - 2:36

score 71 · Answer 10 · 2026-03-25 16:20:54

71

Views

Must continuous surjection $f:\Bbb Z[\frac16]\to\Bbb Z[\frac16]$, fixed in $\lvert\cdot\rvert_3$, stabilise to approach $0$?

Published on 25 Mar 2026 - 16:20

score 312 · Answer 11 · 2026-03-25 12:33:51

312

Views

Types of undefined for removable discontinuities and vertical asymptotes

Published on 25 Mar 2026 - 12:33

score 115 · Answer 12 · 2026-03-26 08:14:35

115

Views

$f$ is uniformly continuity

Published on 26 Mar 2026 - 8:14

score 803 · Answer 13 · 2026-03-27 23:39:43

803

Views

Showing that a function is continuous, using polar coordinates.

Published on 27 Mar 2026 - 23:39

score 144 · Answer 14 · 2018-08-06 19:59:20

144

Views

"Switching" of a continuous function

Published on 06 Aug 2018 - 19:59

score 43 · Answer 15 · 2018-08-07 12:35:07

43

Views

On continuous extension of Thomae function.

Published on 07 Aug 2018 - 12:35

List Question

For metric space $(X, d)$ and fixed $a\in X$, prove function from induced topology to $\Bbb R$ defined by $f(x) = d(a, x)$ is continuous.

Differential Equations Proof for Equilibrium

Is there a name for a "continuous space of sequences"?

Linear transformation in space of infinite dimension

$M$ equicontinuous and closed set of $C([a,b],\mathbb{R})$. There is $m \geq 0$ such that $|f(a)| \leq m$ $\forall f$. Prove that $M$ is compact

How to compute $\lim_{x \to 0} \frac{1}{x^2} \int_{0}^{x} f(t)t \space dt $?

Show that there exists no $f_0\in X$ such that $||f_0||=1$ and $\text{dist}(f_0,Y)=1$

Continuity and differentiability at (0,0)

$C(K, K)$ equipped with certain topology compact?

Must continuous surjection $f:\Bbb Z[\frac16]\to\Bbb Z[\frac16]$, fixed in $\lvert\cdot\rvert_3$, stabilise to approach $0$?

Types of undefined for removable discontinuities and vertical asymptotes

$f$ is uniformly continuity

Showing that a function is continuous, using polar coordinates.

"Switching" of a continuous function

On continuous extension of Thomae function.

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