Question

Correct non-inductive proof of Euler's Formula $|V|+|F|-|E|=2$?

score 377 · Answer 1 · 2026-05-11 01:34:51

377

Views

Correct non-inductive proof of Euler's Formula $|V|+|F|-|E|=2$?

Published on 11 May 2026 - 1:34

score 296 · Answer 2 · 2026-04-11 04:09:06

296

Views

Proof Check: Outer Regularity of Lebesgue Measure

Published on 11 Apr 2026 - 4:09

score 60 · Answer 3 · 2026-04-17 00:16:04

Let $\{a_n\}_n$ be a sequence and suppose $\{a_n\}_n$ isn't bounded above. Prove that there's a subsequence $\{a_{n_k} \}_k$ such that $a_{n_k} → ∞.$

score 126 · Answer 4 · 2026-04-15 17:17:47

126

Views

Prove that topological space $ X= {[0,1]}^{2} $ with dictionary order topology is not second countable. (my solution)

Published on 15 Apr 2026 - 17:17

score 104 · Answer 5 · 2026-04-30 05:04:41

104

Views

Equivalence with measurable functions and spaces

Published on 30 Apr 2026 - 5:04

score 2k · Answer 6 · 2026-04-30 05:05:07

2k

Views

Function $F$ is surjective if and only if $F$ is $1-1$

Published on 30 Apr 2026 - 5:05

score 535 · Answer 7 · 2026-04-12 09:59:48

535

Views

Prove that $\textbf{Int}(Y)$ is the largest open set contained in $Y$

Published on 12 Apr 2026 - 9:59

score 63 · Answer 8 · 2026-04-14 02:51:56

63

Views

Counterexample: linearly ordered sets for which there exists more than one isomorphism

Published on 14 Apr 2026 - 2:51

score 67 · Answer 9 · 2026-04-16 07:25:05

67

Views

A step in a proof that $M, N\unlhd G$ implies $MN\unlhd G$.

Published on 16 Apr 2026 - 7:25

score 54 · Answer 10 · 2026-04-15 12:50:38

54

Views

$A$ $9\times 9$ real matrix such that $A^3=0$ and $A^{i}\neq 0$ for $i=1$ and $2$. what is the number of possible J.C. Forms(upto similarity) of $A$.

Published on 15 Apr 2026 - 12:50

score 620 · Answer 11 · 2026-04-18 02:58:44

620

Views

Is my proof of $\binom{m+n}{r}=\binom{m}{0}\binom{n}{r} + \binom{m}{1}\binom{n}{r-1} + ... + \binom{m}{r}\binom{n}{0}$ right?

Published on 18 Apr 2026 - 2:58

score 321 · Answer 12 · 2026-04-11 02:01:59

321

Views

Product of compact metric spaces is again compact.

Published on 11 Apr 2026 - 2:01

score 1.3k · Answer 13 · 2026-04-11 18:15:59

1.3k

Views

Limit of a sequence multiply by a constant

Published on 11 Apr 2026 - 18:15

score 56 · Answer 14 · 2026-04-15 08:11:50

56

Views

Expressing $\frac{\partial u}{\partial t}=k\frac{\partial^2 u}{\partial x^2}+S(x,t)$ as an integral involving $S(x,t)$

Published on 15 Apr 2026 - 8:11

score 37 · Answer 15 · 2026-04-14 14:57:23

37

Views

Limiting behavior of a meromorphic function

Published on 14 Apr 2026 - 14:57

List Question

Correct non-inductive proof of Euler's Formula $|V|+|F|-|E|=2$?

Proof Check: Outer Regularity of Lebesgue Measure

Let $\{a_n\}_n$ be a sequence and suppose $\{a_n\}_n$ isn't bounded above. Prove that there's a subsequence $\{a_{n_k} \}_k$ such that $a_{n_k} → ∞.$

Prove that topological space $ X= {[0,1]}^{2} $ with dictionary order topology is not second countable. (my solution)

Equivalence with measurable functions and spaces

Function $F$ is surjective if and only if $F$ is $1-1$

Prove that $\textbf{Int}(Y)$ is the largest open set contained in $Y$

Counterexample: linearly ordered sets for which there exists more than one isomorphism

A step in a proof that $M, N\unlhd G$ implies $MN\unlhd G$.

$A$ $9\times 9$ real matrix such that $A^3=0$ and $A^{i}\neq 0$ for $i=1$ and $2$. what is the number of possible J.C. Forms(upto similarity) of $A$.

Is my proof of $\binom{m+n}{r}=\binom{m}{0}\binom{n}{r} + \binom{m}{1}\binom{n}{r-1} + ... + \binom{m}{r}\binom{n}{0}$ right?

Product of compact metric spaces is again compact.

Limit of a sequence multiply by a constant

Expressing $\frac{\partial u}{\partial t}=k\frac{\partial^2 u}{\partial x^2}+S(x,t)$ as an integral involving $S(x,t)$

Limiting behavior of a meromorphic function

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