Question

Is $(I^n, \partial I^n)$ homotopy equivalent to $(R^n, R^n\setminus \left\{0\right\})$

score 710 · Answer 1 · 2026-04-15 01:35:18

710

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Is $(I^n, \partial I^n)$ homotopy equivalent to $(R^n, R^n\setminus \left\{0\right\})$

Published on 15 Apr 2026 - 1:35

score 257 · Answer 2 · 2026-05-10 15:03:25

257

Views

Bipartite graph $G=(A,B)$ with $\delta(A)=3n/2$ and no $C_4$ has a matching which saturate each vertex in $A$.

Published on 10 May 2026 - 15:03

score 1.7k · Answer 3 · 2026-04-09 04:21:12

1.7k

Views

Is the product of path connected spaces also path connected in a topology other than the product topology?

Published on 09 Apr 2026 - 4:21

score 140 · Answer 4 · 2026-04-16 18:54:20

140

Views

Evaluate $\lim\limits_{x\to 0 } \frac{ e^{\frac{\ln(1+ax)}{x}} - e^{\frac{a\ln(1+x)}{x}}}{x}$.

Published on 16 Apr 2026 - 18:54

score 175 · Answer 5 · 2026-04-17 15:22:21

175

Views

The implication: $x+\frac{1}{x}=1 \implies x^7+\frac{1}{x^7}=1$

Published on 17 Apr 2026 - 15:22

score 6.2k · Answer 6 · 2026-04-16 00:22:03

6.2k

Views

A die is weighted so that each even number is twice as likely to appear as any odd number.

Published on 16 Apr 2026 - 0:22

score 244 · Answer 7 · 2026-04-17 15:21:22

Ten students, $A, B, \ldots,$ are in a class. If a committee of 3 is chosen at random from the class, find the probability that $A$ is chosen.

score 1.6k · Answer 8 · 2026-04-16 09:06:04

1.6k

Views

Find the probability that the maximum of the two numbers is greater than $4$.

Published on 16 Apr 2026 - 9:06

score 262 · Answer 9 · 2026-04-15 08:10:53

262

Views

If $a$ and $b$ are generators of the group $G$ and $ab=ba,$ Prove that $G$ is abelian.

Published on 15 Apr 2026 - 8:10

score 778 · Answer 10 · 2026-05-10 10:22:48

778

Views

Prove that composition of analytic functions is analytic

Published on 10 May 2026 - 10:22

score 150 · Answer 11 · 2026-04-14 17:23:44

150

Views

Prove $\ \int_a^b fd\alpha =0$

Published on 14 Apr 2026 - 17:23

score 331 · Answer 12 · 2026-04-17 11:56:31

Prove that if $\mathcal F \subseteq \mathcal{G}_1 \cap \mathcal{G}_2$, then $\cap \mathcal{G}_1 \cup \cap \mathcal{G}_2 \subseteq \cap \mathcal{F}$

score 617 · Answer 13 · 2026-04-15 15:39:28

617

Views

Which function satisfies $: \mathbb R → [−2, 2]$ with $((0))^ 2 + ( ′ (0))^ 2 = 85$,also $f$ is twice differentiable?

Published on 15 Apr 2026 - 15:39

score 561 · Answer 14 · 2026-04-29 12:53:17

561

Views

Integral of $e^{-xy}$ is a Dirac Delta

Published on 29 Apr 2026 - 12:53

score 338 · Answer 15 · 2026-04-13 00:37:37

338

Views

Proving the Fundamental Theorem of Algebra via Taylor Series?

Published on 13 Apr 2026 - 0:37

List Question

Is $(I^n, \partial I^n)$ homotopy equivalent to $(R^n, R^n\setminus \left\{0\right\})$

Bipartite graph $G=(A,B)$ with $\delta(A)=3n/2$ and no $C_4$ has a matching which saturate each vertex in $A$.

Is the product of path connected spaces also path connected in a topology other than the product topology?

Evaluate $\lim\limits_{x\to 0 } \frac{ e^{\frac{\ln(1+ax)}{x}} - e^{\frac{a\ln(1+x)}{x}}}{x}$.

The implication: $x+\frac{1}{x}=1 \implies x^7+\frac{1}{x^7}=1$

A die is weighted so that each even number is twice as likely to appear as any odd number.

Ten students, $A, B, \ldots,$ are in a class. If a committee of 3 is chosen at random from the class, find the probability that $A$ is chosen.

Find the probability that the maximum of the two numbers is greater than $4$.

If $a$ and $b$ are generators of the group $G$ and $ab=ba,$ Prove that $G$ is abelian.

Prove that composition of analytic functions is analytic

Prove $\ \int_a^b fd\alpha =0$

Prove that if $\mathcal F \subseteq \mathcal{G}_1 \cap \mathcal{G}_2$, then $\cap \mathcal{G}_1 \cup \cap \mathcal{G}_2 \subseteq \cap \mathcal{F}$

Which function satisfies $: \mathbb R → [−2, 2]$ with $((0))^ 2 + ( ′ (0))^ 2 = 85$,also $f$ is twice differentiable?

Integral of $e^{-xy}$ is a Dirac Delta

Proving the Fundamental Theorem of Algebra via Taylor Series?

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