This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (April 2014) (Learn how and when to remove this template message)
In mathematics, a condensation point p of a subset S of a topological space, is any point p such that every open neighborhood of p contains uncountably many points of S. Thus "condensation point" is synonymous with "-accumulation point".
- If S = (0,1) is the open unit interval, a subset of the real numbers, then 0 is a condensation point of S.
- If S is an uncountable subset of a set X endowed with the indiscrete topology, then any point p of X is a condensation point of X as the only open neighborhood of p is X itself.
- Walter Rudin, Principles of Mathematical Analysis, 3rd Edition, Chapter 2, exercise 27
- John C. Oxtoby, Measure and Category, 2nd Edition (1980),
- Lynn Steen and J. Arthur Seebach, Jr., Counterexamples in Topology, 2nd Edition, pg. 4
|This topology-related article is a stub. You can help Wikipedia by expanding it.|