Question

Why is $\arg z$ continuous on the arc of the unit circle of those points with $|\arg z |< \frac{1}{2}\pi$

score 62 · Answer 1 · 2019-02-06 20:21:33

62

Views

Why is $\arg z$ continuous on the arc of the unit circle of those points with $|\arg z |< \frac{1}{2}\pi$

Published on 06 Feb 2019 - 20:21

score 51 · Answer 2 · 2019-02-06 21:29:37

51

Views

Under what conditions does $f(z)$ continuous imply $\arg(f(z))$ continuous?

Published on 06 Feb 2019 - 21:29

score 106 · Answer 3 · 2019-02-07 12:14:30

106

Views

Multivariable Limit: how to prove it exists?

Published on 07 Feb 2019 - 12:14

score 60 · Answer 4 · 2019-02-07 19:38:07

60

Views

An inequality between two continuous functions defines a set with non-empty interior?

Published on 07 Feb 2019 - 19:38

score 89 · Answer 5 · 2026-04-01 16:21:32

89

Views

Continuity of a function (upper envelope)

Published on 01 Apr 2026 - 16:21

score 75 · Answer 6 · 2019-02-08 09:52:33

75

Views

Is it true that $\varinjlim\left( A_{i}\times B\right)\cong \left(\varinjlim A_{i}\right)\times B$ in topological spaces?

Published on 08 Feb 2019 - 9:52

score 2.1k · Answer 7 · 2019-02-08 10:16:58

2.1k

Views

Continuity of function defined on natural numbers

Published on 08 Feb 2019 - 10:16

score 32 · Answer 8 · 2026-03-25 22:23:35

32

Views

Continuity of a function on $\mathbb{R}^n\times\mathbb{R}^n$

Published on 25 Mar 2026 - 22:23

score 82 · Answer 9 · 2026-03-29 21:54:04

82

Views

Proving discontinuity at $x=0$ for $f(x)=\sum_{n=0}^{\infty} \sin^{2}(nx)/ (1+n^{2} x^{2})$

Published on 29 Mar 2026 - 21:54

score 3.9k · Answer 10 · 2026-03-25 07:42:28

3.9k

Views

Hölder exponents greater than 1 imply function to be constant?

Published on 25 Mar 2026 - 7:42

score 163 · Answer 11 · 2019-02-08 20:41:18

163

Views

How to prove using elementary methods that this function is everywhere continuous but nowhere differentiable?

Published on 08 Feb 2019 - 20:41

score 128 · Answer 12 · 2026-03-26 07:55:08

128

Views

Does there exist a triple point map?

Published on 26 Mar 2026 - 7:55

score 189 · Answer 13 · 2019-02-09 16:04:23

189

Views

When the glue rule fails, is it a given that $f(x)$ at a given point isn’t continuous?

Published on 09 Feb 2019 - 16:04

score 42 · Answer 14 · 2026-04-06 11:53:56

42

Views

Metric spaces and continous functions.

Published on 06 Apr 2026 - 11:53

score 380 · Answer 15 · 2026-03-25 16:03:30

380

Views

Is the family of all continuous functions from a compact metric space to a separable complete metric space separable?

Published on 25 Mar 2026 - 16:03

List Question

Why is $\arg z$ continuous on the arc of the unit circle of those points with $|\arg z |< \frac{1}{2}\pi$

Under what conditions does $f(z)$ continuous imply $\arg(f(z))$ continuous?

Multivariable Limit: how to prove it exists?

An inequality between two continuous functions defines a set with non-empty interior?

Continuity of a function (upper envelope)

Is it true that $\varinjlim\left( A_{i}\times B\right)\cong \left(\varinjlim A_{i}\right)\times B$ in topological spaces?

Continuity of function defined on natural numbers

Continuity of a function on $\mathbb{R}^n\times\mathbb{R}^n$

Proving discontinuity at $x=0$ for $f(x)=\sum_{n=0}^{\infty} \sin^{2}(nx)/ (1+n^{2} x^{2})$

Hölder exponents greater than 1 imply function to be constant?

How to prove using elementary methods that this function is everywhere continuous but nowhere differentiable?

Does there exist a triple point map?

When the glue rule fails, is it a given that $f(x)$ at a given point isn’t continuous?

Metric spaces and continous functions.

Is the family of all continuous functions from a compact metric space to a separable complete metric space separable?

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