Question

f takes finitely many values, and is continuous at a show that f is constant on an interval nigh of a

score 143 · Answer 1 · 2018-10-29 17:54:13

f takes finitely many values, and is continuous at a show that f is constant on an interval nigh of a

Published on 29 Oct 2018 - 17:54

score 58 · Answer 2 · 2018-10-29 22:15:37

Let $f$ be defined and monotonic increasing on $(a,b)$. Suppose for any open $E\subset (a,b)$, $f(E)$ is open. Prove $f$ is continuous.

score 47 · Answer 3 · 2018-10-29 23:08:49

47

Views

Establishing Continuity of $\cos x$ based on Continuity of $\sin x$

Published on 29 Oct 2018 - 23:08

score 101 · Answer 4 · 2018-10-29 23:28:29

Exist $f : \mathbb { R } \rightarrow \mathbb { R }$ such that $f (x)f (y) = f (x+ y) \forall x , y \in \mathbb { R }$ , but $f$ is not continuous?

score 412 · Answer 5 · 2018-10-30 01:40:28

412

Views

Rationale for why a function is continuous at its isolated points

Published on 30 Oct 2018 - 1:40

score 60 · Answer 6 · 2018-10-30 03:39:33

60

Views

If $\lim_{h\to 0}[f(x+h)-f(x+h)]=0$ for all $x$ then $f$ is not necessarily continuous

Published on 30 Oct 2018 - 3:39

score 118 · Answer 7 · 2018-10-30 03:51:47

118

Views

Where is $k(z)=PV(z-1)^{\frac{1}{2}}PV(z+1)^{\frac{1}{2}}$ Continuous and Differentiable

Published on 30 Oct 2018 - 3:51

score 86 · Answer 8 · 2018-10-30 06:33:35

86

Views

Let $f \in C[a,b]$ and $g(x)$ be real-valued on $[a,b]$. If $g(x) = f(x)$ a.e in $[a,b]$. Is $g(x)$ a.e. continuous?

Published on 30 Oct 2018 - 6:33

score 104 · Answer 9 · 2018-10-30 07:17:51

104

Views

Prove this function cannot be continuous

Published on 30 Oct 2018 - 7:17

score 24 · Answer 10 · 2018-10-30 09:51:57

24

Views

A family of non-Lipschitzian functions with a prescribed number of global minimuns

Published on 30 Oct 2018 - 9:51

score 49 · Answer 11 · 2018-10-30 12:50:46

49

Views

Is a function differentiable at a point if a certain limit exists

Published on 30 Oct 2018 - 12:50

score 72 · Answer 12 · 2026-03-26 14:29:29

72

Views

Why does this argument that sin(1/x) is not uniform continuous on (0,1) fail for [0,1]?

Published on 26 Mar 2026 - 14:29

score 42 · Answer 13 · 2018-10-30 15:55:01

42

Views

Check Continuity of ${y=x^2\sin\left(\frac{1}{x}\right),x\neq0 \& y=0 for x=0} at x=0$.

Published on 30 Oct 2018 - 15:55

score 76 · Answer 14 · 2026-03-25 14:22:46

76

Views

Best Lipschitz constant for IVP with two variables $u$ and $t$ with an initial condition and interval for $t$?

Published on 25 Mar 2026 - 14:22

score 66 · Answer 15 · 2026-03-25 05:56:51

66

Views

If $x\in dom(\phi),$ we can use the code $\Phi$ and minimization theorem to prove within $RCA_0$ that $\phi(x)$ exists.

Published on 25 Mar 2026 - 5:56

List Question

f takes finitely many values, and is continuous at a show that f is constant on an interval nigh of a

Let $f$ be defined and monotonic increasing on $(a,b)$. Suppose for any open $E\subset (a,b)$, $f(E)$ is open. Prove $f$ is continuous.

Establishing Continuity of $\cos x$ based on Continuity of $\sin x$

Exist $f : \mathbb { R } \rightarrow \mathbb { R }$ such that $f (x)f (y) = f (x+ y) \forall x , y \in \mathbb { R }$ , but $f$ is not continuous?

Rationale for why a function is continuous at its isolated points

If $\lim_{h\to 0}[f(x+h)-f(x+h)]=0$ for all $x$ then $f$ is not necessarily continuous

Where is $k(z)=PV(z-1)^{\frac{1}{2}}PV(z+1)^{\frac{1}{2}}$ Continuous and Differentiable

Let $f \in C[a,b]$ and $g(x)$ be real-valued on $[a,b]$. If $g(x) = f(x)$ a.e in $[a,b]$. Is $g(x)$ a.e. continuous?

Prove this function cannot be continuous

A family of non-Lipschitzian functions with a prescribed number of global minimuns

Is a function differentiable at a point if a certain limit exists

Why does this argument that sin(1/x) is not uniform continuous on (0,1) fail for [0,1]?

Check Continuity of ${y=x^2\sin\left(\frac{1}{x}\right),x\neq0 \& y=0 for x=0} at x=0$.

Best Lipschitz constant for IVP with two variables $u$ and $t$ with an initial condition and interval for $t$?

If $x\in dom(\phi),$ we can use the code $\Phi$ and minimization theorem to prove within $RCA_0$ that $\phi(x)$ exists.

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