Prove that given collection of subset is a topology.
7678
Show "countable complement topology" is a topology
55486
Topological proof to show a complement set of a set is polygonally connected
110744
How to prove that a compact set in a Hausdorff topological space is closed?
58004
showing a collection of sets contain all closed sets
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
146146
Proof that a closed subset of a compact space is a compact space
124234
Prove that if $X$ and it's closure $\overline X$ are connected and if $X\subset Y \subset \overline X$, show that Y is also connected.
137621
The Number of Topologies on a Finite Set
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
109374
Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
144383
The closure of a connected set in a topological space is connected
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
103717
Topological Property of the Set of Integers
135025
Axiomatization of a Topology using the Boundary
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$