power of the continuum

power of the continuum

[′pau̇·ər əvthə kən′tin·yə·wəm]
(mathematics)
The cardinality of the set of real numbers.
References in periodicals archive ?
Pawlicowski [5] presented a forcing free proof of a conjecture of Mycielski [4] that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the continuum. In [1], Biss equipped the loop space of X with the compact open topology.
Then [[pi].sub.n](X) is either finitely generated or has the power of the continuum.
Moreover, [[pi].sup.top.sub.n](X) is not discrete if and only if [[pi].sub.n](X) has the power of the continuum.