List questions from separation-axioms | MathQA

For every closed set $F$ in a completely regular space $X,$ does there exist a nonzero continuous function $f:X\to [0,1]$ such that $f=0$ outside $F?$

Published on 05 Jan 2019 - 12:01

For a closed $G_\delta$ set $F\subseteq X,$ does there exist a continuous function $f:X\to [0,1]$ such that $f=0$ on $F$ and $f\neq 0$ outside $F?$

Published on 05 Jan 2019 - 12:51

Does there exist a continuous function separating these two sets $A$ and $B$

Published on 11 Jan 2019 - 20:25

What does it mean if you take the zero vector in the hyperplane separation theorem?

Published on 15 Jan 2019 - 20:32

Separating points in a compact Hausdorff space.

Published on 21 Jan 2019 - 23:30

Prime Integer Topology is $T_2$ but not $T_3$

Published on 30 Jan 2019 - 15:29

Locally compact Hausdorff then Tychonoff

Published on 03 Feb 2019 - 5:29

Prove that the function $f:X\to I=[0,1]$ by $f(x)=\min\{\frac{d(x,C)}{d(p,C)},1\}$ is continuous on $X$.

Published on 04 Feb 2019 - 17:57

Compact group acting on regular space

Published on 10 Feb 2019 - 23:05

How do I prove $U (A_1)\cap V (A_2) \neq \emptyset$? Can You help me to find where do we arrive contradiction?

Published on 11 Feb 2019 - 9:18

$T_0$-space iff for each pair of $a$ and $b$ distinct members of X, $\overline{\{a\}}\neq\overline{\{b\}}$

Published on 11 Feb 2019 - 15:33

Is a completely regular space whose convergent sequences are eventually constant discrete?

Published on 11 Feb 2019 - 23:27

How do I prove that there exists a bijection from power set of $D$ to $C'\subseteq C.$

Published on 23 Feb 2026 - 12:06

Nested interestection forms neighbourhood basis

Published on 22 Mar 2026 - 23:28

An equivalent condition for being $T_1-$space $(X,\mathscr T)$ is normal.

Published on 12 Feb 2019 - 14:58