Interior (topology)

Inner point, justice or open core are terms from topology, a branch of mathematics.

Each element of a subset of a topological space to which an environment can be found in, lying entirely within, is an interior point of. The set of all interior points of affairs is called or open core of.

Example: Consider a circular disk as part of the level, then the points on the edge of the circle no interior points ( but boundary points ). In contrast, all points between the edge of the circle and the circle center and the circle center are even interior points of the circular area.

Definition

Be an arbitrary subset of a topological space. Then a point is exactly then an interior point of, if a surrounding area of ​​at is, that is, if there is a subset that contains and is open.

The set of all interior points of affairs is called or open core of; it is the largest open subset of. Is usually denoted with or especially in English-language literature using or.

Properties

  • A subset of a topological space if and only open when it is equal to its interior.
  • The interior of the complement is the complement of the financial statements, and vice versa:

The interior of the complement is also called the exterior of M. The space X that is divided into interior, boundary and exterior of M.

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