Namespaces
Variants
Actions

Difference between revisions of "Isolated point"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (better)
m (→‎References: isbn link)
 
Line 8: Line 8:
 
====References====
 
====References====
 
<table>
 
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1978). ''Counterexamples in Topology'' (second edition).  Berlin, New York: Springer-Verlag. ISBN 978-0-486-68735-3. MR 507446.  Zbl 0386.54001.</TD></TR>
+
<TR><TD valign="top">[1]</TD> <TD valign="top">  Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1978). ''Counterexamples in Topology'' (second edition).  Berlin, New York: Springer-Verlag. {{ISBN|978-0-486-68735-3}} {{MR|507446}} {{ZBL|0386.54001}}</TD></TR>
 
</table>
 
</table>

Latest revision as of 08:27, 23 November 2023

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

[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. URL: http://encyclopediaofmath.org/index.php?title=Isolated_point&oldid=54567
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