Homeomorphism


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homeomorphism

[¦hō·mē·ə¦mȯr‚fiz·əm]
(mathematics)
A continuous map between topological spaces which is one-to-one, onto, and its inverse function is continuous. Also known as bicontinuous function; topological mapping.

Homeomorphism

 

one of the basic concepts of topology. Two figures (more precisely, two topological spaces) are said to be homeomorphic if there exists a one-to-one continuous mapping of any one onto the other, for which the inverse mapping is also continuous. In this case, the mapping itself is called a homeomorphism. For example, any circle is homeomorphic to any square; any two segments are homeomorphic, but a segment is not homeomorphic to a circle or a line. A line is homeomorphic to any interval (that is, a segment without end points). The concept of homeomorphism is the basis for defining the extremely important concept of a topological property. Specifically, a property of a figure F is said to be topological if it is found in all figures homeomorphic to F. Examples of topological properties are compactness and connectedness.

A. V. ARKHANGEL’SKII

References in periodicals archive ?
For each tile [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we choose a planar embedding in the following way: For [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the homeomorphism [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] must be orientation-preserving, and the vertex of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which corresponds to [p.
Maki, semi-Generalized Homeomorphisms and Generalized semi-Homeomorphismin topological spaces, IJPAM, 26(1995), No.
n-m] respectively, so H is a topological group homeomorphism.
Piotrowski (1979) further investigated semi homeomorphisms and Noiri & Ahmad (1985) introduced semi-weakly continuous functions and these functions were further characterized by Dorsett (1990).
Again by the Lebesgue dominated convergence theorem, the integral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] because [empty set] is a homeomorphism.
phi]] defined to be the pull-back, via a homeomorphism [phi] : P(X) [?
c) the map [absolute value of K'] [right arrow] [absolute value of K] extending the map of vertices of K' to their corresponding points of [absolute value of K], is a homeomorphism.
Theorem 1: Every homeomorphism is a pre [alpha] g* closed map.
Homeomorphism is the function through which a coffee cup can be reshaped into a donut: "a function that is a one-to-one mapping between sets such that both the function and its inverse are continuous and that in topology exists for geometric figures which can be transformed one into the other by an elastic deformation" (Merriam-Webster).
Keywords and Phrases: [alpha]-finitistic space, Sum space, Homeomorphism, Good extension property.
By first addressing the constraints of homeomorphism, the author appeals to the approach of comparison and translation to explain the difficulty of leaving a pluralistic world for a Judeo-Christian Western world that relies on monism.
To prove the negative norm estimate for the pressure, we recall that the divergence operator is a homeomorphism from [H.