Question

Continuous mapping onto itself s.t. $f(A) = A$ where $A$ is closed

score 443 · Answer 1 · 2026-03-25 11:22:54

443

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Continuous mapping onto itself s.t. $f(A) = A$ where $A$ is closed

Published on 25 Mar 2026 - 11:22

score 88 · Answer 2 · 2026-03-26 06:18:23

88

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Does continuity on $S$ implies continuity on $\partial S$?

Published on 26 Mar 2026 - 6:18

score 69 · Answer 3 · 2018-06-23 08:03:27

69

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How $f\circ g$ is discontinuous at $x=2$?

Published on 23 Jun 2018 - 8:03

score 76 · Answer 4 · 2018-06-23 10:56:24

Let $A \subset \Bbb R$ be an $F_\sigma$ set. Construct a function $f$ such that it precisely has $A$ as it's set of discontinuity.

score 149 · Answer 5 · 2026-03-24 23:44:46

149

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Piecewise union of continuous maps is continuous

Published on 24 Mar 2026 - 23:44

score 3.4k · Answer 6 · 2018-06-23 23:16:01

3.4k

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Can a continuous function have discontinuities?

Published on 23 Jun 2018 - 23:16

score 90 · Answer 7 · 2018-06-24 15:14:48

90

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Left and right limits of $f$

Published on 24 Jun 2018 - 15:14

score 54 · Answer 8 · 2018-06-25 06:09:39

54

Views

Question about boundedness of a continuous function $f$ without using open cover and its finite subcover.

Published on 25 Jun 2018 - 6:09

score 216 · Answer 9 · 2018-06-25 07:27:34

216

Views

How to prove that a binary function is continuous?

Published on 25 Jun 2018 - 7:27

score 49 · Answer 10 · 2026-03-26 06:32:58

49

Views

Clarity on Question About Continuity and Uniform Continuity

Published on 26 Mar 2026 - 6:32

score 1.8k · Answer 11 · 2018-06-25 18:39:45

1.8k

Views

Number of points of discontinuity of $[5x]+\{3x\}$

Published on 25 Jun 2018 - 18:39

score 175 · Answer 12 · 2018-06-26 05:59:20

175

Views

Looking for a function $f$ that is continuous in a point, yet has an infinite derivative in this point

Published on 26 Jun 2018 - 5:59

score 695 · Answer 13 · 2026-03-26 06:29:03

695

Views

Uniform continuity of a function on closure of a set, where it is uniformly continuous.

Published on 26 Mar 2026 - 6:29

score 128 · Answer 14 · 2018-06-26 18:56:14

128

Views

show that $f(x) = \frac{1}{1+e^{\frac{1}{n!\pi x}}}$ can be made discontinuous at any rational point in interval (0,1) by proper selection of n

Published on 26 Jun 2018 - 18:56

score 96 · Answer 15 · 2018-06-26 19:34:51

96

Views

A question on continuity of functions

Published on 26 Jun 2018 - 19:34

List Question

Continuous mapping onto itself s.t. $f(A) = A$ where $A$ is closed

Does continuity on $S$ implies continuity on $\partial S$?

How $f\circ g$ is discontinuous at $x=2$?

Let $A \subset \Bbb R$ be an $F_\sigma$ set. Construct a function $f$ such that it precisely has $A$ as it's set of discontinuity.

Piecewise union of continuous maps is continuous

Can a continuous function have discontinuities?

Left and right limits of $f$

Question about boundedness of a continuous function $f$ without using open cover and its finite subcover.

How to prove that a binary function is continuous?

Clarity on Question About Continuity and Uniform Continuity

Number of points of discontinuity of $[5x]+\{3x\}$

Looking for a function $f$ that is continuous in a point, yet has an infinite derivative in this point

Uniform continuity of a function on closure of a set, where it is uniformly continuous.

show that $f(x) = \frac{1}{1+e^{\frac{1}{n!\pi x}}}$ can be made discontinuous at any rational point in interval (0,1) by proper selection of n

A question on continuity of functions

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