# Cactoid

From Encyclopedia of Mathematics

A locally connected continuum that is the closure of the sum of at most a countable number of spheres and simple arcs located in Euclidean space , and such that for each closed contour there exists exactly one sphere containing it. Cactoids, and they alone, are monotone images of the -dimensional sphere ; also, every cactoid is a monotone open image of .

**How to Cite This Entry:**

Cactoid.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Cactoid&oldid=12209

This article was adapted from an original article by B.A. Efimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article