An exercise on a characterization of the existence of an interior point

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 A of a topological space X meets each dense subset of X if and only if the interior of A is not empty.

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Une réflexion sur “An exercise on a characterization of the existence of an interior point

  1. Pingback: A characterization of the existence of an interior point | Formalis Mathematica

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