Question

Continuity at a point of a piecewise function

score 100 · Answer 1 · 2018-11-14 23:50:22

100

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Continuity at a point of a piecewise function

Published on 14 Nov 2018 - 23:50

score 38 · Answer 2 · 2026-03-26 06:34:20

38

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What is the best that you can say about a function with given property

Published on 26 Mar 2026 - 6:34

score 49 · Answer 3 · 2018-11-15 15:26:27

49

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continuous function on a set of infimums

Published on 15 Nov 2018 - 15:26

score 56 · Answer 4 · 2026-03-26 17:53:58

56

Views

Let $ f : X \to Y $ a biyective funtion and uniformly continuous.

Published on 26 Mar 2026 - 17:53

score 807 · Answer 5 · 2018-11-16 01:45:23

807

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Let $f:\mathbb{I} \to \mathbb{R}$ continuous function such that $f(0)=f(1)$.

Published on 16 Nov 2018 - 1:45

score 91 · Answer 6 · 2026-03-26 17:53:28

91

Views

Proof that if f(a)<0 and f(b)>0 f and is continuous on [a,b] then f changes sign at some c in (a,b) Part 2

Published on 26 Mar 2026 - 17:53

score 74 · Answer 7 · 2026-03-26 17:52:25

74

Views

Consider the series $\sum_{n=1}^\infty \frac{(-1)^n}{n+x}$

Published on 26 Mar 2026 - 17:52

score 387 · Answer 8 · 2026-03-26 03:10:42

387

Views

characteristic function of a clopen set continuous?

Published on 26 Mar 2026 - 3:10

score 46 · Answer 9 · 2018-11-16 12:00:12

A periodic function $f$ over $R$ (with the minimal postive period $\mu>0$), show $\lim_{n\to\infty} f(n)$ does not exist.

score 43 · Answer 10 · 2026-04-04 08:46:25

43

Views

Let $f(x_1', ..., x_n')$ and $g_1(x_1), ..., g_n(x_n)$ be continuous functions. Is $f(g_1(x_1), ..., g_n(x_n))$ continuous?

Published on 04 Apr 2026 - 8:46

score 80 · Answer 11 · 2018-11-17 06:11:02

80

Views

Verifying the continuity of a piecewise-defined, composite function.

Published on 17 Nov 2018 - 6:11

score 582 · Answer 12 · 2018-11-17 06:20:44

582

Views

Let $f,g : X\to X$ be real continuous functions such that $f(X)\cap g(X) = \emptyset$ and $f(X)\cup g(X) = X$. Which sets cannot be equal to $X$?

Published on 17 Nov 2018 - 6:20

score 48 · Answer 13 · 2018-11-17 11:31:08

48

Views

Is $\sqrt{x^3}$ uniformly continuous?

Published on 17 Nov 2018 - 11:31

score 146 · Answer 14 · 2026-03-25 17:40:33

146

Views

An Example of a Non-continuous Injection on a Real Interval, that is Not Strictly Monotonic.

Published on 25 Mar 2026 - 17:40

score 82 · Answer 15 · 2026-03-26 10:43:35

82

Views

Find a strictly decreasing $f:(0,1) \to [0, \infty]$ such that $f(0^{+})= \infty$, $f(1)=0$ and $f(u^2)=2 f(u)$.

Published on 26 Mar 2026 - 10:43

List Question

Continuity at a point of a piecewise function

What is the best that you can say about a function with given property

continuous function on a set of infimums

Let $ f : X \to Y $ a biyective funtion and uniformly continuous.

Let $f:\mathbb{I} \to \mathbb{R}$ continuous function such that $f(0)=f(1)$.

Proof that if f(a)<0 and f(b)>0 f and is continuous on [a,b] then f changes sign at some c in (a,b) Part 2

Consider the series $\sum_{n=1}^\infty \frac{(-1)^n}{n+x}$

characteristic function of a clopen set continuous?

A periodic function $f$ over $R$ (with the minimal postive period $\mu>0$), show $\lim_{n\to\infty} f(n)$ does not exist.

Let $f(x_1', ..., x_n')$ and $g_1(x_1), ..., g_n(x_n)$ be continuous functions. Is $f(g_1(x_1), ..., g_n(x_n))$ continuous?

Verifying the continuity of a piecewise-defined, composite function.

Let $f,g : X\to X$ be real continuous functions such that $f(X)\cap g(X) = \emptyset$ and $f(X)\cup g(X) = X$. Which sets cannot be equal to $X$?

Is $\sqrt{x^3}$ uniformly continuous?

An Example of a Non-continuous Injection on a Real Interval, that is Not Strictly Monotonic.

Find a strictly decreasing $f:(0,1) \to [0, \infty]$ such that $f(0^{+})= \infty$, $f(1)=0$ and $f(u^2)=2 f(u)$.

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