Proper cycle
From Encyclopedia of Mathematics
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=11895
Proper cycle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Proper_cycle&oldid=11895
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