Question

Prove that a subset is open relative to another subset (Proof Verification)

score 95 · Answer 1 · 2020-05-05 19:58:20

95

Views

Prove that a subset is open relative to another subset (Proof Verification)

Published on 05 May 2020 - 19:58

score 40 · Answer 2 · 2020-05-05 20:00:42

40

Views

For any $x_{0}\in X$ and $r > 0$, then the ball $B(x_{0},r)$ is an open set. The set $\{x\in X\mid d(x,x_{0})\leq r\}$ is a closed set.

Published on 05 May 2020 - 20:00

score 70 · Answer 3 · 2026-03-30 02:11:48

70

Views

Solve $- \Delta_pu = |u|^{q - 2}u$ via the Ekeland Variational Principle - Is my solution correct?

Published on 30 Mar 2026 - 2:11

score 104 · Answer 4 · 2026-04-03 03:19:10

104

Views

If $E_{1},E_{2},\ldots,E_{n}$ are a finite collection of open sets in $X$, then $E_{1}\cap E_{2}\cap\ldots\cap E_{n}$ is also open.

Published on 03 Apr 2026 - 3:19

score 27 · Answer 5 · 2026-04-09 05:15:12

27

Views

Limit Points and Infinite Subsets of a Compact Set (Proof Verification)

Published on 09 Apr 2026 - 5:15

score 325 · Answer 6 · 2026-04-12 07:52:21

325

Views

Prove inverse of odd function is odd

Published on 12 Apr 2026 - 7:52

score 198 · Answer 7 · 2020-05-05 23:57:23

198

Views

If $E$ is a subset of $X$, then $E$ is open if and only if the complement $X\backslash E = \{x\in X\mid x\not\in E\}$ is closed.

Published on 05 May 2020 - 23:57

score 903 · Answer 8 · 2020-05-06 02:18:33

903

Views

Monotone convergence theorem for a real function?

Published on 06 May 2020 - 2:18

score 1.1k · Answer 9 · 2026-03-30 20:42:52

1.1k

Views

Computing Covariance of Sums of i.i.d. Random Variables

Published on 30 Mar 2026 - 20:42

score 113 · Answer 10 · 2020-05-06 05:57:18

113

Views

Proving a sequence $(a_n)$ converges under certain conditions

Published on 06 May 2020 - 5:57

score 63 · Answer 11 · 2020-05-06 06:01:20

63

Views

$\frac{x^2 -4}{x-4} \rightarrow -5$ as $x \rightarrow 3$, proving the limit from first principles. ($\delta - \epsilon$).

Published on 06 May 2020 - 6:01

score 75 · Answer 12 · 2020-05-06 07:05:42

75

Views

Longest Sequence of Ones and Borel-Cantelli Lemma

Published on 06 May 2020 - 7:05

score 740 · Answer 13 · 2026-04-11 19:24:09

740

Views

Find the closed path of given system of ordinary differential equation

Published on 11 Apr 2026 - 19:24

score 66 · Answer 14 · 2026-04-10 19:52:28

66

Views

Proof verification :"For some" or "for all"

Published on 10 Apr 2026 - 19:52

score 55 · Answer 15 · 2020-05-06 16:20:34

55

Views

Prove that $\forall A \exists !B \big (B \subseteq A \wedge \forall C(C \subseteq A \rightarrow B \vartriangle C = A \setminus C)\big)$

Published on 06 May 2020 - 16:20

List Question

Prove that a subset is open relative to another subset (Proof Verification)

For any $x_{0}\in X$ and $r > 0$, then the ball $B(x_{0},r)$ is an open set. The set $\{x\in X\mid d(x,x_{0})\leq r\}$ is a closed set.

Solve $- \Delta_pu = |u|^{q - 2}u$ via the Ekeland Variational Principle - Is my solution correct?

If $E_{1},E_{2},\ldots,E_{n}$ are a finite collection of open sets in $X$, then $E_{1}\cap E_{2}\cap\ldots\cap E_{n}$ is also open.

Limit Points and Infinite Subsets of a Compact Set (Proof Verification)

Prove inverse of odd function is odd

If $E$ is a subset of $X$, then $E$ is open if and only if the complement $X\backslash E = \{x\in X\mid x\not\in E\}$ is closed.

Monotone convergence theorem for a real function?

Computing Covariance of Sums of i.i.d. Random Variables

Proving a sequence $(a_n)$ converges under certain conditions

$\frac{x^2 -4}{x-4} \rightarrow -5$ as $x \rightarrow 3$, proving the limit from first principles. ($\delta - \epsilon$).

Longest Sequence of Ones and Borel-Cantelli Lemma

Find the closed path of given system of ordinary differential equation

Proof verification :"For some" or "for all"

Prove that $\forall A \exists !B \big (B \subseteq A \wedge \forall C(C \subseteq A \rightarrow B \vartriangle C = A \setminus C)\big)$

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