TOPICS
Search

Compactum


A compactum (plural: compacta) is a compact metric space.

An example of a compactum is any finite discrete metric space. Also, the space [0,1] union [2,3] is a compactum, with the usual metric inherited from the real line. Notice that this latter example is a compactum that is not a continuum, because it is not connected. A continuum is a connected compactum.


See also

Continuum, Metric Space

This entry contributed by Matt Insall (author's link)

Explore with Wolfram|Alpha

References

Charatonik, J. J. and Prajs, J. R. "On Local Connectedness of Absolute Retracts." Pacific J. Math. 201, 83-88, 2001.

Referenced on Wolfram|Alpha

Compactum

Cite this as:

Insall, Matt. "Compactum." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Compactum.html

Subject classifications