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 ?
The study of partial dynamical systems, that is, dynamical systems originating from the action of a partially defined homeomorphism on a topological space, was benefited strongly from the theory of partial group actions and partial crossed products; the most influential article in this direction is due to Exel, Laca and Quigg [45].
Moreover, I define SBT property and hereditary SBT by SBT homeomorphism and investigate the relations between these concepts.
Sundaram studied generalized continuous functions and generalized homeomorphism.
Definition 6 (Billingsley metric) Let [LAMBDA] be the collection of all homeomorphisms [lambda]: [0,1] [right arrow] [0,1], with [lambda](0) = 0 and [lambda](1) = 1 satisfying
Piotrowski (1979) further investigated semi homeomorphisms and Noiri & Ahmad (1985) introduced semi-weakly continuous functions and these functions were further characterized by Dorsett (1990).
Expansive homeomorphisms and hyperbolic diffeomorphisms on 3-manifolds.
Let F(L) denote the set of all sense-preserving plane homeomorphisms f of regions D [contains] L such that f(L) is a line segment or circle and let
and these singular fibers are quotients of the homogeneous space by distinguished groups of homeomorphisms.
Among the topics are Branner-Hubbard motions and attracting dynamics, examples of Feigenbaum Julia sets with small Hausdorff dimension, Sierpinski carpets and gaskets as Julia sets of rational maps, homeomorphisms of the Mandelbrot set, Arnold disks and the moduli of Herman rings of the complex standard family, and stretching rays and their accumulations following Pia Willumsen.
KELLOGG, On homeomorphisms for an elliptic equation in domains with corners,, Differential Integral Equations, 8 (1995), pp.
r], r) with each other using the homeomorphisms [F.
We denote by F(L) the set of all sense preserving plane homeomorphisms f of the region D [contains] L such that f (L) is a line segment (or circle) and let