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continuum (Definition)

A continuum is a compact connected topological space. Some authors impose additional conditions and require that the space be nondegenerate, Hausdorff, or metric.

Bibliography

SS
Lynn Arthur Steen and J. Arthur Seebach, Jr, Counterexamples in Topology, Springer-Verlag, 1978, p. 33
HY
John G. Hocking, and Gail S. Young, Topology, Dover Publications, New York, 1988, p. 43
G
Steven A. Gaal, Point Set Topology, Academic Press, New York, 1964, p. 103
MCG
Michael C. Gemignani, Elementary Topology, 2nd ed. Dover Publications, New York, 1990, p. 202
NEW
M.H.A. Newman, Elements of the Topology of Plane Sets of Points, Cambridge University Press, 1964, p. 71
W
Stephen Willard, General Topology, Addison-Wesley, Reading, MA, 1970, p. 203
WI
Raymond Louis Wilder, Topology of Manifolds, Amer. Math. Society, Providence, RI, 1963, p. 36
MI
J. van Mill, G.M. Reed, editors, Open Problems in Topology, North-Holland, Amsterdam, 1990, p. 305




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Cross-references: metric, Hausdorff, nondegenerate, topological space, connected, compact
There are 2 references to this entry.

This is version 2 of continuum, born on 2008-12-18, modified 2008-12-18.
Object id is 11358, canonical name is Continuum3.
Accessed 395 times total.

Classification:
AMS MSC54F15 (General topology :: Special properties :: Continua and generalizations)

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