Definition:Continuum

Definition

A continuum is an object which is continuous.

Topology

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

Real Numbers

The real number line is an example of a continuum.

Time

Time, as best we understand it as a physical quantity, is an example of a continuum.

Ideal Fluid

An ideal fluid is an example of a continuum.

Spacetime

Spacetime, as best we understand it as a physical quantity, is an example of a continuum.

Also see

• Results about continua can be found here.

Linguistic Note

The plural of continuum is continua, although the technically-erroneous form continuums can occasionally be found.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuum: 1. (plural continua)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuum: 1. (plural continua)