If a set is open, does it mean that every point is an interior point?
7871
Are "if" and "iff" interchangeable in definitions?
73338
Prove that the closure of complement, is the complement of the interior
157753
Show that any set in a metric space can be written as the intersection of open sets
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
25171
Why does a convex set have the same interior points as its closure?
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
116009
Proving that if a set is both open and closed then it is equal to the real numbers
16056
Is empty set element of every set if it is subset of every set?
50506
What concept does an open set axiomatise?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
84104
Definition of neighborhood and open set in topology
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?
28523
When would the intersection of the empty set mean anything?
125233
Why is an open interval not a compact set?
88823
How can the empty set be open in the definition of the cofinite topology?
110845
Convex Set with Empty Interior Lies in an Affine Set