Definition:Continuum/Topology
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be both compact and connected in $T$.
Then $H$ is a continuum.
Examples
Closed Real Interval
A closed real interval is a continuum.
Closed Ball
A closed ball is a continuum.
Also see
Linguistic Note
The plural of continuum is continua, although the technically-erroneous form continuums can occasionally be found.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness: Biconnectedness and Continua
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuum: 2. (plural continua)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuum: 2. (plural continua)