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Topology

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Moderate

Calculation of Cardinality

TOPO-WZGYGP

Let $L$ be the $\mathbb{R}$-vector space of real valued functions on $\mathbb{R}$.

Which of the following sets has the same cardinality as its dual $L^*$?

A

$\mathbb{R}$

B

$\mathbb{Q}$

C

The set of total orders on $\mathbb{R}$

D

The set of subsets of the power set of $\mathbb{R}$