Question

Real valued function which is continuous only on transcendental numbers

score 91 · Answer 1 · 2026-03-25 12:16:21

91

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Real valued function which is continuous only on transcendental numbers

Published on 25 Mar 2026 - 12:16

score 311 · Answer 2 · 2026-03-25 21:48:19

311

Views

If f is a uniform continuous function on (a,b), then f is bounded on (a,b).

Published on 25 Mar 2026 - 21:48

score 903 · Answer 3 · 2026-03-28 08:36:25

903

Views

Continuity of $\begin{cases}(xy+y^2)/(x^4+y^2)&\text{if }(x,y)\neq(0,0),\\0&\text{if }(x,y)=(0,0)\end{cases}$ at origin using polar coordinates

Published on 28 Mar 2026 - 8:36

score 648 · Answer 4 · 2026-03-26 14:42:25

648

Views

Determine whether the function $f(x) = e^x \cos (1/x)$ is uniformly continuous on $A = (0,1)$.

Published on 26 Mar 2026 - 14:42

score 302 · Answer 5 · 2026-03-29 17:26:59

302

Views

GRE 0568 #65: Disprove 'There is a continuous one-to-one function from $(0,1)$ onto $[0,1].$'

Published on 29 Mar 2026 - 17:26

score 96 · Answer 6 · 2026-04-01 09:37:51

96

Views

Is this proof of the existence of the general $n$-th root in $\mathbb{R}$ legitimate?

Published on 01 Apr 2026 - 9:37

score 1k · Answer 7 · 2018-10-25 17:58:28

1k

Views

Is $\frac{x^2y^2}{\sqrt{x^2+y^2}}$ continuous?

Published on 25 Oct 2018 - 17:58

score 61 · Answer 8 · 2026-03-28 12:48:32

61

Views

Is $|\frac{y}{x^2}|\exp(- |\frac{y}{x^2}|)$ continuous?

Published on 28 Mar 2026 - 12:48

score 131 · Answer 9 · 2018-10-25 19:59:35

131

Views

Is $|x+y|/\sqrt{x^2+y^2}$ continuous?

Published on 25 Oct 2018 - 19:59

score 53 · Answer 10 · 2018-10-25 20:21:02

53

Views

Proof $g \circ f: D \to\mathbb{R}^k$ with $(g \circ f) (x) := g(f(x))$ continuous

Published on 25 Oct 2018 - 20:21

score 158 · Answer 11 · 2018-10-25 20:39:24

158

Views

Let X be a topological space and $f_1, . . . , f_n : X → \mathbb{R}$ be continuous functions.

Published on 25 Oct 2018 - 20:39

score 88 · Answer 12 · 2026-03-25 13:13:30

88

Views

Proving $f: \mathbb{R}^n \ni x\to \left\lVert x \right\rVert$ $\in \mathbb{R}$ to be continuous

Published on 25 Mar 2026 - 13:13

score 139 · Answer 13 · 2026-03-26 14:27:47

139

Views

a problem about continuous functions on closed intervals

Published on 26 Mar 2026 - 14:27

score 401 · Answer 14 · 2018-10-26 01:03:51

401

Views

Proving the difference quotient has a removable discontinuity

Published on 26 Oct 2018 - 1:03

score 118 · Answer 15 · 2026-03-22 12:38:55

118

Views

Differentiability of a multi variable function.

Published on 22 Mar 2026 - 12:38

List Question

Real valued function which is continuous only on transcendental numbers

If f is a uniform continuous function on (a,b), then f is bounded on (a,b).

Continuity of $\begin{cases}(xy+y^2)/(x^4+y^2)&\text{if }(x,y)\neq(0,0),\\0&\text{if }(x,y)=(0,0)\end{cases}$ at origin using polar coordinates

Determine whether the function $f(x) = e^x \cos (1/x)$ is uniformly continuous on $A = (0,1)$.

GRE 0568 #65: Disprove 'There is a continuous one-to-one function from $(0,1)$ onto $[0,1].$'

Is this proof of the existence of the general $n$-th root in $\mathbb{R}$ legitimate?

Is $\frac{x^2y^2}{\sqrt{x^2+y^2}}$ continuous?

Is $|\frac{y}{x^2}|\exp(- |\frac{y}{x^2}|)$ continuous?

Is $|x+y|/\sqrt{x^2+y^2}$ continuous?

Proof $g \circ f: D \to\mathbb{R}^k$ with $(g \circ f) (x) := g(f(x))$ continuous

Let X be a topological space and $f_1, . . . , f_n : X → \mathbb{R}$ be continuous functions.

Proving $f: \mathbb{R}^n \ni x\to \left\lVert x \right\rVert$ $\in \mathbb{R}$ to be continuous

a problem about continuous functions on closed intervals

Proving the difference quotient has a removable discontinuity

Differentiability of a multi variable function.

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