Question

Other solution to 'compact and continuous imply uniformly continuous'

score 45 · Answer 1 · 2026-03-25 11:01:03

45

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Extending continuous functions from almost everywhere to everywhere

Published on 23 Mar 2026 - 2:43

score 109 · Answer 3 · 2018-03-13 04:40:05

109

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Show that the set of non-$\beta$-Hölder functions is dense in the space of $\alpha$-Hölder function, $0<\alpha<\beta<1$

Published on 13 Mar 2018 - 4:40

score 104 · Answer 4 · 2026-03-24 22:44:33

104

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Show that the addition function for two elements in $\mathbb{R}^\omega$ is continuous

Published on 24 Mar 2026 - 22:44

score 47 · Answer 5 · 2018-03-14 10:56:33

47

Views

Show that if $f$ is surjective, then $\overline{f(A)} = Y$.

Published on 14 Mar 2018 - 10:56

score 159 · Answer 6 · 2018-03-15 12:26:10

159

Views

Understanding a limiting procedure

Published on 15 Mar 2018 - 12:26

score 231 · Answer 7 · 2018-03-15 13:21:31

If $f:[a, b] \to \mathbb{R}$ is a continuous function, s.t. $f(x)>0$ for all $x$, prove that there exists $c >0$, s.t. $f(x) > c$ for all $x$.

score 201 · Answer 8 · 2018-03-15 15:10:49

201

Views

Let $ f:(-1,1)\to(-1,1)$ be continuous, $f(x)=f(x^2)$ for every $x$ then the value of $f(\frac 1 4)$

Published on 15 Mar 2018 - 15:10

score 63 · Answer 9 · 2026-03-29 05:50:11

63

Views

Existence of another critical point

Published on 29 Mar 2026 - 5:50

score 30 · Answer 10 · 2018-03-15 19:38:05

30

Views

A confusion in checking differentiability at a point x=1. Cannot find what to write in place of $f(1-h)$ or $f(1+h)$

Published on 15 Mar 2018 - 19:38

score 128 · Answer 11 · 2026-03-29 05:49:56

128

Views

Existence of a critical point between two local minimum

Published on 29 Mar 2026 - 5:49

score 44 · Answer 12 · 2026-03-29 05:44:07

44

Views

$x_{1}$ and $x_{2}$ roots of $f$ with $f'(x_{1}) \gt 0$ and $f'(x_{2}) \gt 0$. Existence of another root between $(x_{1},x_{2})$.

Published on 29 Mar 2026 - 5:44

score 410 · Answer 13 · 2026-03-25 11:52:53

410

Views

Why are continuous partial derivatives a sufficient condition for differentiability?

Published on 25 Mar 2026 - 11:52

score 871 · Answer 14 · 2018-03-16 03:52:06

871

Views

Real Analysis - Limits and Continuity of Piecewise Function

Published on 16 Mar 2018 - 3:52

score 53 · Answer 15 · 2018-03-16 05:58:48

Find $f : [0,1] \to \mathbb R$ s.t. $\{x \in [0,1]$, for all neighborhood of $x$, there exist $y$ and $z$ in it s.t. $f(y)f(z)<0 \}\ $ is uncountable

List Question

Other solution to 'compact and continuous imply uniformly continuous'

Extending continuous functions from almost everywhere to everywhere

Show that the set of non-$\beta$-Hölder functions is dense in the space of $\alpha$-Hölder function, $0<\alpha<\beta<1$

Show that the addition function for two elements in $\mathbb{R}^\omega$ is continuous

Show that if $f$ is surjective, then $\overline{f(A)} = Y$.

Understanding a limiting procedure

If $f:[a, b] \to \mathbb{R}$ is a continuous function, s.t. $f(x)>0$ for all $x$, prove that there exists $c >0$, s.t. $f(x) > c$ for all $x$.

Let $ f:(-1,1)\to(-1,1)$ be continuous, $f(x)=f(x^2)$ for every $x$ then the value of $f(\frac 1 4)$

Existence of another critical point

A confusion in checking differentiability at a point x=1. Cannot find what to write in place of $f(1-h)$ or $f(1+h)$

Existence of a critical point between two local minimum

$x_{1}$ and $x_{2}$ roots of $f$ with $f'(x_{1}) \gt 0$ and $f'(x_{2}) \gt 0$. Existence of another root between $(x_{1},x_{2})$.

Why are continuous partial derivatives a sufficient condition for differentiability?

Real Analysis - Limits and Continuity of Piecewise Function

Find $f : [0,1] \to \mathbb R$ s.t. $\{x \in [0,1]$, for all neighborhood of $x$, there exist $y$ and $z$ in it s.t. $f(y)f(z)<0 \}\ $ is uncountable

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