“Condensation point”的意思、由来-开放百科全书

词条

Condensation point

释义

Examples
References

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".^[1]

Examples

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.

References

1. ^https://www.encyclopediaofmath.org/index.php/Condensation_point_of_a_set

* 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

2 : Mathematical objects|Topology

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