We recall that, in a topological space, a point is said to be an interior point of a subset if the latter is a neighborhood of the point in question. The set of interior points of a subset is called the interior of this subset. It is well-known that a subset is open if and only if it coincides which its interior. In this note, we invite to prove a characterization of the existence of at least an interior point of a set.
Exercise.
Prove that a subset of a topological space
meets each dense subset of
if and only if the interior of
is not empty.
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