Intersection of neighborhood of identity is closure of identity.
14532
Closure of identity element in a topological group is the intersection of its neighborhood system
81550
Linking two theorems: on algebraic closure and on minimal splitting field
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
144383
The closure of a connected set in a topological space is connected
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
122086
continuous function: preimage of closure of a set is closure of preimage
127900
Interior of closure of open set in topological space
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
73338
Prove that the closure of complement, is the complement of the interior
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
109649
idempotents acting as local identities
108740
$C^1[a,b]$ is closed in $C[a,b]$
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
154259
Countinuity of the identity map between different topologies
79213
Proof about a Topological space being arc connect