Proving that $\overline{S \cap U} = \overline U$ if $U$ open and $S$ dense
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
90590
Prove that the following set is dense
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
9268
Proving that the Union of Two Compact Sets is Compact
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
14576
$(U\cap W)^0 = U^0 + W^0$
55366
Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected.
97064
Dense set in an infinite cofinite space
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
16654
Unions and Intersections of Open Sets are Open
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?