Topology

This page is a sub-page of our page on Mathematical Concepts.

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Related KMR pages:

Oscar Reutersvärd
M.C. Escher

Disambiguation
Entropy
Function
Homology and Cohomology
Homotopy
Space
Time
Quotients
Duality
Topology
Uncertainty
Dimension

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A structure that implements openness
is called a topology.

An open set has no boundary.
Every one of its member elements
is always “interior” of it,
that is, each point is contained in a neighborhood of points
that also belong to the open set.

The complement of an open set
is called a closed set.

In contrast to an open set
a closed set has a boundary
and if the closed set is also compact
then it behaves much like a closed interval
with respect to convergence of a sequence:
Any sequence of members that tries to converge
will succeed.

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