Question

Let $f$ be continuous real-valued function on $[0,1]$. Then, $F(x)=\max\{f(t):0\leq t\leq x\}$ is continuous

score 428 · Answer 1 · 2026-03-26 06:15:19

428

Views

Let $f$ be continuous real-valued function on $[0,1]$. Then, $F(x)=\max\{f(t):0\leq t\leq x\}$ is continuous

Published on 26 Mar 2026 - 6:15

score 77 · Answer 2 · 2026-03-26 11:18:08

77

Views

Let $f$ be a nonnegative continuous function on $[a,b]$, then $ \lim\limits_{n\to \infty} \left[\int^{b}_{a}f^{n}(x)dx\right]^{\frac{1}{n}}=M$

Published on 26 Mar 2026 - 11:18

score 115 · Answer 3 · 2026-03-26 13:01:19

115

Views

Let $f:[a,b]\to\Bbb{R}$ be continuous. Does $\max\{|f(x)|:a\leq x\leq b\}$ exist?

Published on 26 Mar 2026 - 13:01

score 121 · Answer 4 · 2026-03-25 11:31:41

121

Views

Is the derivative of a Lipschitz continuous gradient function is a continuous vector function?

Published on 25 Mar 2026 - 11:31

score 94 · Answer 5 · 2026-03-25 06:05:51

94

Views

$f(t)=\text{det}(A+tB)$ is continuous for symmetric positive semi-definite matrices $A$ and $B$?

Published on 25 Mar 2026 - 6:05

score 665 · Answer 6 · 2018-09-09 16:23:54

665

Views

Nilpotent element in Ring of continuous function.

Published on 09 Sep 2018 - 16:23

score 39 · Answer 7 · 2018-09-09 17:46:31

39

Views

Question on Intermediate Value Theorem

Published on 09 Sep 2018 - 17:46

score 1.5k · Answer 8 · 2026-03-30 07:05:47

1.5k

Views

Is a positive, monotone and sub-additive function concave?

Published on 30 Mar 2026 - 7:05

score 383 · Answer 9 · 2018-09-10 09:09:25

383

Views

Prove piecewise function is only continuous at $x=0$

Published on 10 Sep 2018 - 9:09

score 237 · Answer 10 · 2018-09-10 12:05:02

237

Views

Closure and continuous map

Published on 10 Sep 2018 - 12:05

score 2.4k · Answer 11 · 2026-03-29 01:33:40

2.4k

Views

Continuity preserves connectedness

Published on 29 Mar 2026 - 1:33

score 602 · Answer 12 · 2026-03-28 22:55:08

602

Views

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Published on 28 Mar 2026 - 22:55

score 887 · Answer 13 · 2026-03-25 23:36:00

887

Views

Does there exist a continuous bijection from real line onto the unit circle?

Published on 25 Mar 2026 - 23:36

score 54 · Answer 14 · 2018-09-11 13:08:44

54

Views

Reasoning out the existence of a limit of a piecewise-defined function in order to prove discontinuity

Published on 11 Sep 2018 - 13:08

score 78 · Answer 15 · 2026-03-27 14:00:36

78

Views

Continuity and a finite borel measure

Published on 27 Mar 2026 - 14:00

List Question

Let $f$ be continuous real-valued function on $[0,1]$. Then, $F(x)=\max\{f(t):0\leq t\leq x\}$ is continuous

Let $f$ be a nonnegative continuous function on $[a,b]$, then $ \lim\limits_{n\to \infty} \left[\int^{b}_{a}f^{n}(x)dx\right]^{\frac{1}{n}}=M$

Let $f:[a,b]\to\Bbb{R}$ be continuous. Does $\max\{|f(x)|:a\leq x\leq b\}$ exist?

Is the derivative of a Lipschitz continuous gradient function is a continuous vector function?

$f(t)=\text{det}(A+tB)$ is continuous for symmetric positive semi-definite matrices $A$ and $B$?

Nilpotent element in Ring of continuous function.

Question on Intermediate Value Theorem

Is a positive, monotone and sub-additive function concave?

Prove piecewise function is only continuous at $x=0$

Closure and continuous map

Continuity preserves connectedness

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Does there exist a continuous bijection from real line onto the unit circle?

Reasoning out the existence of a limit of a piecewise-defined function in order to prove discontinuity

Continuity and a finite borel measure

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