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Proper cycle

From Encyclopedia of Mathematics
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in a metric space

A sequence of -cycles (cf. Vietoris homology) satisfying the condition as . The compact set on which all vertices of all cycles of all simplices of a proper cycle lie is called the compact support of . If is a continuous mapping, then is also a proper cycle, and a deformation of induces a deformation of the proper cycle.

Cf. Vietoris homology.

How to Cite This Entry:
Proper cycle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Proper_cycle&oldid=48333
This article was adapted from an original article by A.A. Mal'tsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article