Isolated point
From Encyclopedia of Mathematics - Reading time: 1 min
of a subspace $A$ of a topological space $X$
A point $a\in A$ such that the intersection of some neighbourhood of $a$ with $A$ consists of the point $a$ alone.
A subset $A$ with no isolated points is dense-in-itself; a closed dense-in-itself subset is a perfect set.
References[edit]
| [1] | Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1978). Counterexamples in Topology (second edition). Berlin, New York: Springer-Verlag. ISBN 978-0-486-68735-3 MR507446 Zbl 0386.54001 |
How to Cite This Entry: Isolated point (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Isolated_point8 views | ↧ Download this article as ZWI file
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