Question

Show that on any uncountable set $X$, there is a metric on $X$ with respect to which $X$ is not separable

score 119 · Answer 1 · 2026-03-29 08:15:00

119

Views

Show that on any uncountable set $X$, there is a metric on $X$ with respect to which $X$ is not separable

Published on 29 Mar 2026 - 8:15

score 593 · Answer 2 · 2026-04-13 03:34:38

593

Views

When does $ |{x}|^\alpha\sin{\frac1{x}} $ have continuous derivative at zero?

Published on 13 Apr 2026 - 3:34

score 246 · Answer 3 · 2018-01-24 19:17:49

246

Views

Differential of the product map

Published on 24 Jan 2018 - 19:17

score 32 · Answer 4 · 2026-04-11 11:06:53

32

Views

Is not enough for a sequence being monotonic and bounded for $n \geq n_0$?

Published on 11 Apr 2026 - 11:06

score 1.1k · Answer 5 · 2026-04-06 17:19:09

1.1k

Views

$\lim \sup$ and $\lim \inf$ of root and ratio test sequences of a series (Rudin)

Published on 06 Apr 2026 - 17:19

score 653 · Answer 6 · 2026-04-09 11:57:27

653

Views

A function which is not equal almost everywhere (wrt Lebesgue measure) to a continuous function and not almost everywhere continuous function

Published on 09 Apr 2026 - 11:57

score 92 · Answer 7 · 2026-03-25 09:27:43

92

Views

Prove through induction that $\sum_{a=1}^{b}a(b-a)=\frac{b(b-1)(b+6)}{6}$

Published on 25 Mar 2026 - 9:27

score 279 · Answer 8 · 2026-04-12 11:44:41

279

Views

Inequality in the proof of Picard Iterations

Published on 12 Apr 2026 - 11:44

score 720 · Answer 9 · 2026-03-31 20:08:14

720

Views

How do you show $f(x,y)=\left( \frac{x}{x^2+y^2},\frac{y}{x^2+y^2}\right)$ is a diffeomorphism?

Published on 31 Mar 2026 - 20:08

score 473 · Answer 10 · 2026-04-12 00:46:05

473

Views

Intersection of a sequence of closed intervals

Published on 12 Apr 2026 - 0:46

score 187 · Answer 11 · 2026-03-27 07:31:12

187

Views

Prove that the closure of any uncountable subset of $X$ is all of $X$.

Published on 27 Mar 2026 - 7:31

score 66 · Answer 12 · 2026-04-09 07:32:33

66

Views

For two partitions of an interval any subinterval of the one with the strictly smaller mesh is contained in one or two adjacent ones of the other.

Published on 09 Apr 2026 - 7:32

score 123 · Answer 13 · 2026-04-09 02:55:14

123

Views

Limits of power of fractions

Published on 09 Apr 2026 - 2:55

score 754 · Answer 14 · 2026-03-24 20:32:09

754

Views

Find the derivative of $y=(\tan (x))^{\log (x)}$

Published on 24 Mar 2026 - 20:32

score 79 · Answer 15 · 2026-04-12 18:51:30

79

Views

Every continuous function $f:ℝ\to ℝ$ can be presented as a sum of a certain power series.

Published on 12 Apr 2026 - 18:51

List Question

Show that on any uncountable set $X$, there is a metric on $X$ with respect to which $X$ is not separable

When does $ |{x}|^\alpha\sin{\frac1{x}} $ have continuous derivative at zero?

Differential of the product map

Is not enough for a sequence being monotonic and bounded for $n \geq n_0$?

$\lim \sup$ and $\lim \inf$ of root and ratio test sequences of a series (Rudin)

A function which is not equal almost everywhere (wrt Lebesgue measure) to a continuous function and not almost everywhere continuous function

Prove through induction that $\sum_{a=1}^{b}a(b-a)=\frac{b(b-1)(b+6)}{6}$

Inequality in the proof of Picard Iterations

How do you show $f(x,y)=\left( \frac{x}{x^2+y^2},\frac{y}{x^2+y^2}\right)$ is a diffeomorphism?

Intersection of a sequence of closed intervals

Prove that the closure of any uncountable subset of $X$ is all of $X$.

For two partitions of an interval any subinterval of the one with the strictly smaller mesh is contained in one or two adjacent ones of the other.

Limits of power of fractions

Find the derivative of $y=(\tan (x))^{\log (x)}$

Every continuous function $f:ℝ\to ℝ$ can be presented as a sum of a certain power series.

Trending Questions

Popular # Hahtags

Popular Questions