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Component of a space

From Encyclopedia of Mathematics
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A connected subset \( C \) of a topological space \( X \) with the following property: If \(C_1 \subset X\) is a connected subset such that , then . The components of a space are disjoint. Every non-empty connected subset is contained in exactly one component. If \( C \) is a component of a space \( X \) and , then is a component of . If is a monotone continuous mapping onto, then is a component of if and only if is a component of .

References

[1] K. Kuratowski, "Topology" , 2 , Acad. Press (1968) (Translated from French)
How to Cite This Entry:
Component of a space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Component_of_a_space&oldid=19331
This article was adapted from an original article by B.A. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article