Question

Riemann integrable function implies discontinuous on a Borel set?

score 172 · Answer 1 · 2026-03-25 12:15:03

172

Views

Riemann integrable function implies discontinuous on a Borel set?

Published on 25 Mar 2026 - 12:15

score 325 · Answer 2 · 2026-03-30 03:58:37

325

Views

Must compact bijections be continuous?

Published on 30 Mar 2026 - 3:58

score 40 · Answer 3 · 2026-03-27 01:13:40

40

Views

Determine if the function is uniformly continuous

Published on 27 Mar 2026 - 1:13

score 765 · Answer 4 · 2026-03-27 06:16:58

765

Views

$f: [a,b]\to\Bbb R $. If $g(x)=\sup\{f(t):t∈[a,x]\}$ and $f$ is continuous , then prove that $g$ is continuous at $a$

Published on 27 Mar 2026 - 6:16

score 157 · Answer 5 · 2026-04-01 03:43:22

157

Views

If $f$ is convex function and $f$ is continuous on $(a,b)$.When is $f$ continuous at $a$ and $b$?

Published on 01 Apr 2026 - 3:43

score 111 · Answer 6 · 2026-03-29 12:11:24

111

Views

If $f(x_1)=f(x_2)=y$, then prove that $f$ can not be continuous everywhere

Published on 29 Mar 2026 - 12:11

score 81 · Answer 7 · 2026-03-26 14:42:51

81

Views

$|f(a+h)-2f(a)+f(a-h')|<\varepsilon \Rightarrow f$ is continuous at a

Published on 26 Mar 2026 - 14:42

score 64 · Answer 8 · 2026-04-05 09:53:26

64

Views

Continuity of Function W.R.T. Topology Generated by a Function

Published on 05 Apr 2026 - 9:53

score 537 · Answer 9 · 2026-03-26 23:09:46

537

Views

If $f:[0,1] \rightarrow \mathbb{R}$ is continuous then it is uniformly continuous

Published on 26 Mar 2026 - 23:09

score 45 · Answer 10 · 2026-03-27 21:54:39

45

Views

A question related to the mean value theorem

Published on 27 Mar 2026 - 21:54

score 153 · Answer 11 · 2018-12-20 01:29:37

153

Views

Does there exist a function such that the preimage of $x ^ { 2 } + y ^ { 2 } \leq 1$ is the closed interval $[-1,1]?$

Published on 20 Dec 2018 - 1:29

score 69 · Answer 12 · 2018-12-20 03:42:29

69

Views

Continuity in open intervals

Published on 20 Dec 2018 - 3:42

score 1.7k · Answer 13 · 2026-04-01 05:08:20

1.7k

Views

Can a function be neither convex nor concave everywhere?

Published on 01 Apr 2026 - 5:08

score 1.3k · Answer 14 · 2026-04-05 14:54:15

1.3k

Views

Identity map between metric spaces continuous or not.

Published on 05 Apr 2026 - 14:54

score 59 · Answer 15 · 2018-12-21 22:16:13

59

Views

On uniformly continuous, bounded, hermitian functions whose product is continuously differentiable

Published on 21 Dec 2018 - 22:16

List Question

Riemann integrable function implies discontinuous on a Borel set?

Must compact bijections be continuous?

Determine if the function is uniformly continuous

$f: [a,b]\to\Bbb R $. If $g(x)=\sup\{f(t):t∈[a,x]\}$ and $f$ is continuous , then prove that $g$ is continuous at $a$

If $f$ is convex function and $f$ is continuous on $(a,b)$.When is $f$ continuous at $a$ and $b$?

If $f(x_1)=f(x_2)=y$, then prove that $f$ can not be continuous everywhere

$|f(a+h)-2f(a)+f(a-h')|<\varepsilon \Rightarrow f$ is continuous at a

Continuity of Function W.R.T. Topology Generated by a Function

If $f:[0,1] \rightarrow \mathbb{R}$ is continuous then it is uniformly continuous

A question related to the mean value theorem

Does there exist a function such that the preimage of $x ^ { 2 } + y ^ { 2 } \leq 1$ is the closed interval $[-1,1]?$

Continuity in open intervals

Can a function be neither convex nor concave everywhere?

Identity map between metric spaces continuous or not.

On uniformly continuous, bounded, hermitian functions whose product is continuously differentiable

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