Question

Continuous function of class $C^2$ that consists of cases $0$ if $x\geq 0$, positive if $x<0$

score 73 · Answer 1 · 2018-08-20 13:05:52

73

Views

Continuous function of class $C^2$ that consists of cases $0$ if $x\geq 0$, positive if $x<0$

Published on 20 Aug 2018 - 13:05

score 59 · Answer 2 · 2018-08-20 16:05:10

59

Views

Function that satisfies intermediate value property and $f(x) ≤ f(y)$ for all $x<y$ is continuous

Published on 20 Aug 2018 - 16:05

score 87 · Answer 3 · 2018-08-20 18:40:48

87

Views

Existence of a smooth path connecting two points

Published on 20 Aug 2018 - 18:40

score 92 · Answer 4 · 2018-08-21 08:39:56

92

Views

Characterisation of Continous function using 2 open sets

Published on 21 Aug 2018 - 8:39

score 289 · Answer 5 · 2018-08-21 09:54:08

289

Views

continuity of $f(z)=(z-i)\log(z^2+1)$

Published on 21 Aug 2018 - 9:54

score 453 · Answer 6 · 2018-08-21 11:25:40

453

Views

Question about continuous function.

Published on 21 Aug 2018 - 11:25

score 5.1k · Answer 7 · 2018-08-21 12:35:07

5.1k

Views

A continuous function $f : (0, 1)\to\Bbb R$ and a Cauchy sequence $x_n$ such that $f(x_n)$ is not a Cauchy sequence

Published on 21 Aug 2018 - 12:35

score 89 · Answer 8 · 2026-03-29 01:35:45

89

Views

Is there a continuous surjection from $\Bbb{R}^3\setminus S^2$ to $\Bbb{R}^2\setminus\{(0,0)\}$

Published on 29 Mar 2026 - 1:35

score 131 · Answer 9 · 2018-08-22 04:55:45

131

Views

Function on $[0,1]$ which takes every value twice has infinitely many discontinuities.

Published on 22 Aug 2018 - 4:55

score 1.2k · Answer 10 · 2026-03-25 19:05:01

1.2k

Views

Proving continuity of $\operatorname{Re}(z)$ from the definition

Published on 25 Mar 2026 - 19:05

score 403 · Answer 11 · 2026-04-01 06:31:56

403

Views

Proof of an equivalent criterion for continuous functions in topological spaces

Published on 01 Apr 2026 - 6:31

score 1.1k · Answer 12 · 2026-03-25 10:55:39

1.1k

Views

Is the optimal solution of a convex problem continuous with respect to parameters?

Published on 25 Mar 2026 - 10:55

score 48 · Answer 13 · 2018-08-23 10:21:18

48

Views

How to show that $f : (0,\infty) \to \mathbb{R}^2$ given by $f(t)=(t , \sin(1/t))$ is continuous using open sets?

Published on 23 Aug 2018 - 10:21

score 1.9k · Answer 14 · 2018-08-23 14:21:14

1.9k

Views

What is known about the continuous image of an open set?

Published on 23 Aug 2018 - 14:21

score 484 · Answer 15 · 2026-03-28 23:57:43

484

Views

Mapping disconnected sets onto connected sets

Published on 28 Mar 2026 - 23:57

List Question

Continuous function of class $C^2$ that consists of cases $0$ if $x\geq 0$, positive if $x<0$

Function that satisfies intermediate value property and $f(x) ≤ f(y)$ for all $x<y$ is continuous

Existence of a smooth path connecting two points

Characterisation of Continous function using 2 open sets

continuity of $f(z)=(z-i)\log(z^2+1)$

Question about continuous function.

A continuous function $f : (0, 1)\to\Bbb R$ and a Cauchy sequence $x_n$ such that $f(x_n)$ is not a Cauchy sequence

Is there a continuous surjection from $\Bbb{R}^3\setminus S^2$ to $\Bbb{R}^2\setminus\{(0,0)\}$

Function on $[0,1]$ which takes every value twice has infinitely many discontinuities.

Proving continuity of $\operatorname{Re}(z)$ from the definition

Proof of an equivalent criterion for continuous functions in topological spaces

Is the optimal solution of a convex problem continuous with respect to parameters?

How to show that $f : (0,\infty) \to \mathbb{R}^2$ given by $f(t)=(t , \sin(1/t))$ is continuous using open sets?

What is known about the continuous image of an open set?

Mapping disconnected sets onto connected sets

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