Question

Let $f: D \rightarrow \mathbb{R}$ be strictly increasing. Show that if $f(D)$ is an interval then $f$ is continuous.

score 240 · Answer 1 · 2019-05-09 07:44:57

240

Views

Let $f: D \rightarrow \mathbb{R}$ be strictly increasing. Show that if $f(D)$ is an interval then $f$ is continuous.

Published on 09 May 2019 - 7:44

score 24 · Answer 2 · 2026-04-11 06:43:06

24

Views

Testing assumptions for continuity

Published on 11 Apr 2026 - 6:43

score 644 · Answer 3 · 2026-04-12 03:25:20

644

Views

Find the value of K so that the function is continuous

Published on 12 Apr 2026 - 3:25

score 61 · Answer 4 · 2026-04-11 10:31:19

61

Views

Is it a continuous?

Published on 11 Apr 2026 - 10:31

score 38 · Answer 5 · 2026-04-09 04:10:05

38

Views

Maximal Domain of Continuity

Published on 09 Apr 2026 - 4:10

score 816 · Answer 6 · 2019-05-09 20:30:15

816

Views

How to determine whether a piecewise function with conditions instead of equations has removable discontinuities?

Published on 09 May 2019 - 20:30

score 70 · Answer 7 · 2026-04-11 01:52:11

70

Views

Continuity of Identity Functions Between Metric Spaces

Published on 11 Apr 2026 - 1:52

score 471 · Answer 8 · 2026-04-11 06:43:47

471

Views

The continuous probability dilemma

Published on 11 Apr 2026 - 6:43

score 30 · Answer 9 · 2026-04-10 18:18:13

30

Views

Is it possible to prove that for any non-constant continous real function there is an interval on which the function is strictly monotonous?

Published on 10 Apr 2026 - 18:18

score 32 · Answer 10 · 2019-05-10 15:22:54

32

Views

Is this a valid proof for uniform continuity of $\frac{x^2}{x+1}$?

Published on 10 May 2019 - 15:22

score 31 · Answer 11 · 2019-05-10 22:55:36

31

Views

Determining whether the limit $\lim_{(x,y)\to(0,2)} \frac{x(y-2)^3}{3x-5(y-2)^4}$ exists or not

Published on 10 May 2019 - 22:55

score 83 · Answer 12 · 2026-04-11 03:51:22

83

Views

If $f$ is continous at $c$, prove $\lim_{h \to 0} (\inf \,\{f(x)\mid c \leqslant x \leqslant c+h\})=f(c)$

Published on 11 Apr 2026 - 3:51

score 53 · Answer 13 · 2026-03-25 19:11:59

53

Views

If $f:[0,\infty)\to\mathbb R$ is continuous and $\tau=\inf\left\{t>0:f(t)>\varepsilon\right\}$, then $f(\tau\wedge t)\le\varepsilon$ for all $t\ge0$

Published on 25 Mar 2026 - 19:11

score 863 · Answer 14 · 2026-04-10 05:57:58

863

Views

Is the circle homeomorphic to a $6$ petal rose?

Published on 10 Apr 2026 - 5:57

score 46 · Answer 15 · 2019-05-12 17:25:49

46

Views

Why $f$ may not be continuous despite $\lim_{(x,y)\to (0,0)}f(0,0)=0$?

Published on 12 May 2019 - 17:25

List Question

Let $f: D \rightarrow \mathbb{R}$ be strictly increasing. Show that if $f(D)$ is an interval then $f$ is continuous.

Testing assumptions for continuity

Find the value of K so that the function is continuous

Is it a continuous?

Maximal Domain of Continuity

How to determine whether a piecewise function with conditions instead of equations has removable discontinuities?

Continuity of Identity Functions Between Metric Spaces

The continuous probability dilemma

Is it possible to prove that for any non-constant continous real function there is an interval on which the function is strictly monotonous?

Is this a valid proof for uniform continuity of $\frac{x^2}{x+1}$?

Determining whether the limit $\lim_{(x,y)\to(0,2)} \frac{x(y-2)^3}{3x-5(y-2)^4}$ exists or not

If $f$ is continous at $c$, prove $\lim_{h \to 0} (\inf \,\{f(x)\mid c \leqslant x \leqslant c+h\})=f(c)$

If $f:[0,\infty)\to\mathbb R$ is continuous and $\tau=\inf\left\{t>0:f(t)>\varepsilon\right\}$, then $f(\tau\wedge t)\le\varepsilon$ for all $t\ge0$

Is the circle homeomorphic to a $6$ petal rose?

Why $f$ may not be continuous despite $\lim_{(x,y)\to (0,0)}f(0,0)=0$?

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