Closed or open subsets of $C[a,b]$?
108740
$C^1[a,b]$ is closed in $C[a,b]$
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
125962
The set $A'$ is closed in a $T_1$ space
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
46698
Showing a set is closed under inverses
23225
Union of connected subsets is connected if intersection is nonempty
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
146664
The union of two linearly independent subsets
44623
Closed set as a countable intersection of open sets
106944
Is the set defined by y=sin(1/x) open or closed?
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
79697
If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
22854
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?