Question

If $f(z)$ is continuous and nonzero at a point $z=z_0$, then there is a neighbourhood of $z=z_0$ in which $f(z)$ is nonzero.

score 1.7k · Answer 1 · 2018-10-07 02:58:01

1.7k

Views

If $f(z)$ is continuous and nonzero at a point $z=z_0$, then there is a neighbourhood of $z=z_0$ in which $f(z)$ is nonzero.

Published on 07 Oct 2018 - 2:58

score 154 · Answer 2 · 2026-03-26 09:19:41

Let $(A,<)$ and $(C,\prec)$ be countable, dense, and linearly ordered sets without endpoints. Then $(A,<)$ and $(C,\prec)$ are order-isomorphic

score 254 · Answer 3 · 2018-10-07 04:37:36

254

Views

Prove that $\mathscr B$ is a basis for topology $\mathscr T$ on $\mathbb R$. Is $\mathscr T$ is a usual topology on $\mathbb R$?

Published on 07 Oct 2018 - 4:37

score 68 · Answer 4 · 2018-10-07 05:47:14

68

Views

Proof: infinite parametrisation's of any non-empty subset $\mathbb{R}^n$

Published on 07 Oct 2018 - 5:47

score 333 · Answer 5 · 2026-04-12 07:56:44

333

Views

What is the last digit of $7^{3553}$?

Published on 12 Apr 2026 - 7:56

score 272 · Answer 6 · 2018-10-07 09:08:29

272

Views

If the graphic of $f : X \to Y$ is closed with $Y$ compact and Hausdorff, then $f$ is continuous. [Proof Verification]

Published on 07 Oct 2018 - 9:08

score 643 · Answer 7 · 2026-04-10 21:37:49

643

Views

Armed with a sword and a shield, a proud knight combats a monstrous hydra with 100 heads.

Published on 10 Apr 2026 - 21:37

score 251 · Answer 8 · 2026-03-25 12:54:04

251

Views

k-th exterior power bundle $\Lambda^k(M) = \sqcup_{p\in M}\Lambda^k(\tau(M)_p)$ is a manifold

Published on 25 Mar 2026 - 12:54

score 275 · Answer 9 · 2026-04-09 01:15:51

275

Views

On the series expansion of $\frac{\operatorname{Li}_3(-x)}{1+x}$ and its usage

Published on 09 Apr 2026 - 1:15

score 122 · Answer 10 · 2026-03-25 04:41:07

122

Views

Green's Formula in the case where $M = x^2 - y^2$ and $N=2xy$

Published on 25 Mar 2026 - 4:41

score 1.6k · Answer 11 · 2026-03-26 14:42:30

1.6k

Views

Prove that $\sup(S-T)=\sup S-\inf T$

Published on 26 Mar 2026 - 14:42

score 49 · Answer 12 · 2018-10-08 03:23:49

Suppose that $B$ is a disjoint set of subsets of $\Bbb N$: if $A,A' \in B$ and $A \neq A'$, then $A \cap A' = \emptyset$. Show that B is countable

score 493 · Answer 13 · 2018-10-08 10:12:28

493

Views

Prove that $B$ is basis of Topology on $X\times Y$

Published on 08 Oct 2018 - 10:12

score 414 · Answer 14 · 2026-04-01 14:46:34

414

Views

Let $F$ be a field and consider $F[x, y]$. Show that $(x, y)$ is an ideal of $F[x, y]$.

Published on 01 Apr 2026 - 14:46

score 238 · Answer 15 · 2018-10-08 11:44:40

238

Views

Let $B=\{(a,b]:a,b\in R,a<b\}$ is basis of topology $T$ on $R$ show that each interval$(a,b)$ in open in $(R,T)$

Published on 08 Oct 2018 - 11:44

List Question

If $f(z)$ is continuous and nonzero at a point $z=z_0$, then there is a neighbourhood of $z=z_0$ in which $f(z)$ is nonzero.

Let $(A,<)$ and $(C,\prec)$ be countable, dense, and linearly ordered sets without endpoints. Then $(A,<)$ and $(C,\prec)$ are order-isomorphic

Prove that $\mathscr B$ is a basis for topology $\mathscr T$ on $\mathbb R$. Is $\mathscr T$ is a usual topology on $\mathbb R$?

Proof: infinite parametrisation's of any non-empty subset $\mathbb{R}^n$

What is the last digit of $7^{3553}$?

If the graphic of $f : X \to Y$ is closed with $Y$ compact and Hausdorff, then $f$ is continuous. [Proof Verification]

Armed with a sword and a shield, a proud knight combats a monstrous hydra with 100 heads.

k-th exterior power bundle $\Lambda^k(M) = \sqcup_{p\in M}\Lambda^k(\tau(M)_p)$ is a manifold

On the series expansion of $\frac{\operatorname{Li}_3(-x)}{1+x}$ and its usage

Green's Formula in the case where $M = x^2 - y^2$ and $N=2xy$

Prove that $\sup(S-T)=\sup S-\inf T$

Suppose that $B$ is a disjoint set of subsets of $\Bbb N$: if $A,A' \in B$ and $A \neq A'$, then $A \cap A' = \emptyset$. Show that B is countable

Prove that $B$ is basis of Topology on $X\times Y$

Let $F$ be a field and consider $F[x, y]$. Show that $(x, y)$ is an ideal of $F[x, y]$.

Let $B=\{(a,b]:a,b\in R,a<b\}$ is basis of topology $T$ on $R$ show that each interval$(a,b)$ in open in $(R,T)$

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