Question

Does continuity always imply integrability?

score 9.7k · Answer 1 · 2018-06-20 07:37:22

9.7k

Views

Does continuity always imply integrability?

Published on 20 Jun 2018 - 7:37

score 120 · Answer 2 · 2018-06-20 11:50:33

120

Views

Is $f'(a)$ Not same as Finding Derivative of $f(x)$ and Substituting $x=a$

Published on 20 Jun 2018 - 11:50

score 328 · Answer 3 · 2026-04-01 12:46:23

328

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Is there a continuous bijection from open unit interval to open unit disc?

Published on 01 Apr 2026 - 12:46

score 1k · Answer 4 · 2026-03-25 12:20:55

1k

Views

Is there any continuous function that is only differentiable on $\mathbb{Q}$?

Published on 25 Mar 2026 - 12:20

score 1k · Answer 5 · 2026-03-25 21:47:25

1k

Views

Prime ideals in ring of continuous functions

Published on 25 Mar 2026 - 21:47

score 129 · Answer 6 · 2018-06-20 17:05:03

129

Views

Calculating $\lim_{(x,y)\to(0,0)}f(x,y)$ where $f(x,y)= \begin{cases} \frac{e^x -e^y}{\log(x)-\log(y) } & \ x \neq y\\ xe^x & x=y \end{cases}$

Published on 20 Jun 2018 - 17:05

score 34 · Answer 7 · 2026-03-26 06:32:33

34

Views

Prove that if $f(p)\in I$ then $\exists U\subset\Bbb R$ environment of $p$ such that $f(x)\in I$ $\forall $ $ x \in U$

Published on 26 Mar 2026 - 6:32

score 990 · Answer 8 · 2018-06-21 05:08:39

990

Views

How is continuity of a constant function defined?

Published on 21 Jun 2018 - 5:08

score 46 · Answer 9 · 2018-06-21 10:17:53

46

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$f(x)= (x+y) \sin(\frac{1}{x}+ \frac{1}{y}), x\neq0, y\neq0$ Limit as $x\to0, y\neq0$

Published on 21 Jun 2018 - 10:17

score 861 · Answer 10 · 2018-06-21 19:24:32

861

Views

Coarsest topology where a function is continuous

Published on 21 Jun 2018 - 19:24

score 104 · Answer 11 · 2026-03-25 12:20:37

104

Views

(Dis)continuity of $f(x)=\sum_{j: q_j < x} 2^{-j}$

Published on 25 Mar 2026 - 12:20

score 306 · Answer 12 · 2018-06-22 14:01:53

306

Views

Continuity of Probabilities

Published on 22 Jun 2018 - 14:01

score 824 · Answer 13 · 2018-06-22 15:28:17

824

Views

Continuous function on $[0,1]$, $f(0)=f(1)$

Published on 22 Jun 2018 - 15:28

score 1.2k · Answer 14 · 2026-03-28 23:58:39

1.2k

Views

Proof that $f(x,y) = (x^2 + y^2)\sin(x^2 + y^2)^{-1/2}$ is differentiable?

Published on 28 Mar 2026 - 23:58

score 512 · Answer 15 · 2026-03-26 06:26:23

512

Views

Real Analysis - Uniform continuity

Published on 26 Mar 2026 - 6:26

List Question

Does continuity always imply integrability?

Is $f'(a)$ Not same as Finding Derivative of $f(x)$ and Substituting $x=a$

Is there a continuous bijection from open unit interval to open unit disc?

Is there any continuous function that is only differentiable on $\mathbb{Q}$?

Prime ideals in ring of continuous functions

Calculating $\lim_{(x,y)\to(0,0)}f(x,y)$ where $f(x,y)= \begin{cases} \frac{e^x -e^y}{\log(x)-\log(y) } & \ x \neq y\\ xe^x & x=y \end{cases}$

Prove that if $f(p)\in I$ then $\exists U\subset\Bbb R$ environment of $p$ such that $f(x)\in I$ $\forall $ $ x \in U$

How is continuity of a constant function defined?

$f(x)= (x+y) \sin(\frac{1}{x}+ \frac{1}{y}), x\neq0, y\neq0$ Limit as $x\to0, y\neq0$

Coarsest topology where a function is continuous

(Dis)continuity of $f(x)=\sum_{j: q_j < x} 2^{-j}$

Continuity of Probabilities

Continuous function on $[0,1]$, $f(0)=f(1)$

Proof that $f(x,y) = (x^2 + y^2)\sin(x^2 + y^2)^{-1/2}$ is differentiable?

Real Analysis - Uniform continuity

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