Question

Conditions for $f(x_n,y_n) - f(x_0, y_n) \to 0$ if $(x_n,y_n) \to (x_0,y_0)$?

score 306 · Answer 1 · 2026-03-26 09:50:05

306

Views

Conditions for $f(x_n,y_n) - f(x_0, y_n) \to 0$ if $(x_n,y_n) \to (x_0,y_0)$?

Published on 26 Mar 2026 - 9:50

score 149 · Answer 2 · 2018-07-17 08:55:59

149

Views

If $f:\mathbb R^2\longrightarrow \mathbb R$ continuous, does $\lim_{h\to 0}\int_0^{\infty } f(t+h,x)dx=\int_0^\infty f(t,x)dx$?

Published on 17 Jul 2018 - 8:55

score 91 · Answer 3 · 2026-03-25 20:34:28

91

Views

Continuously chosen points on lines in $\mathbb{R}^{n}$

Published on 25 Mar 2026 - 20:34

score 418 · Answer 4 · 2026-03-25 10:33:17

418

Views

Example of a proper surjection to Hausdorff space that is not perfect?

Published on 25 Mar 2026 - 10:33

score 216 · Answer 5 · 2026-04-01 22:37:24

216

Views

$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly

Published on 01 Apr 2026 - 22:37

score 144 · Answer 6 · 2026-04-01 22:34:49

144

Views

Need help understanding this question about showing continuity in a metric space.

Published on 01 Apr 2026 - 22:34

score 83 · Answer 7 · 2026-03-25 14:24:36

83

Views

Prove that $x_n\to x\implies \liminf\limits_{n\to\infty}f(x_n)\leq f(x)$

Published on 25 Mar 2026 - 14:24

score 78 · Answer 8 · 2018-07-18 07:31:45

78

Views

Prove that $\lim\limits_{x\to 1^{-}}f(x)=-1+\ln 4$ where $f(x)=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{x^{n+1}}{n(n+1)}$

Published on 18 Jul 2018 - 7:31

score 73 · Answer 9 · 2026-03-23 04:25:59

73

Views

Modulus of continuity under homeomorphisms

Published on 23 Mar 2026 - 4:25

score 387 · Answer 10 · 2026-03-27 01:43:16

387

Views

Hour, second and minute hands

Published on 27 Mar 2026 - 1:43

score 4.7k · Answer 11 · 2026-03-25 13:56:18

4.7k

Views

Prove or disprove: If $(x_n)$ is a Cauchy sequence in $X$ and $f$ is a continuous function on $X$, then $(f(x_n))$ is a Cauchy sequence.

Published on 25 Mar 2026 - 13:56

score 1.6k · Answer 12 · 2026-03-29 18:29:40

1.6k

Views

Linear function, that is not continuous?

Published on 29 Mar 2026 - 18:29

score 54 · Answer 13 · 2026-03-26 08:15:05

54

Views

Extension of Uniformly Differentiable function - from open ball to $\mathbb{R}^n$

Published on 26 Mar 2026 - 8:15

score 165 · Answer 14 · 2018-07-19 11:21:02

165

Views

Sequence of continuous functions with discontinuous limits

Published on 19 Jul 2018 - 11:21

score 47 · Answer 15 · 2018-07-19 17:21:07

47

Views

Show that $X$ is the set of points at which the function $f$ is continuous.

Published on 19 Jul 2018 - 17:21

List Question

Conditions for $f(x_n,y_n) - f(x_0, y_n) \to 0$ if $(x_n,y_n) \to (x_0,y_0)$?

If $f:\mathbb R^2\longrightarrow \mathbb R$ continuous, does $\lim_{h\to 0}\int_0^{\infty } f(t+h,x)dx=\int_0^\infty f(t,x)dx$?

Continuously chosen points on lines in $\mathbb{R}^{n}$

Example of a proper surjection to Hausdorff space that is not perfect?

$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly

Need help understanding this question about showing continuity in a metric space.

Prove that $x_n\to x\implies \liminf\limits_{n\to\infty}f(x_n)\leq f(x)$

Prove that $\lim\limits_{x\to 1^{-}}f(x)=-1+\ln 4$ where $f(x)=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{x^{n+1}}{n(n+1)}$

Modulus of continuity under homeomorphisms

Hour, second and minute hands

Prove or disprove: If $(x_n)$ is a Cauchy sequence in $X$ and $f$ is a continuous function on $X$, then $(f(x_n))$ is a Cauchy sequence.

Linear function, that is not continuous?

Extension of Uniformly Differentiable function - from open ball to $\mathbb{R}^n$

Sequence of continuous functions with discontinuous limits

Show that $X$ is the set of points at which the function $f$ is continuous.

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