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A continuum is a compact connected topological space. Some authors impose additional conditions and require that the space be nondegenerate, Hausdorff, or metric.
- 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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"continuum" is owned by Mathprof.
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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 MSC: | 54F15 (General topology :: Special properties :: Continua and generalizations) |
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Pending Errata and Addenda
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