Prove that the interior of the boundary of an open or closed set is empty.
32070
Prove that the Interior of the Boundary is Empty
73130
A simple question about open set
110845
Convex Set with Empty Interior Lies in an Affine Set
149820
How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?
158850
Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
42494
The boundary is a closed set
134999
Writing empty set as union of basis elements for a topology.
110744
How to prove that a compact set in a Hausdorff topological space is closed?
117575
Every proper subspace of a normed vector space has empty interior
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
8414
Proof verification: Set of partial limits of a sequence is closed
65768
What is the cardinality of the set of the empty set?
81351
Polish space in which the interior of each compact set is empty
110677
How is an empty set truly "empty"?
79424
Don't understand proof that interior of a set is open
136755
Direct proof of empty set being subset of every set
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$