Irrational Number Space is Paracompact

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\struct {\R \setminus \Q, \tau_d}$ be the irrational number space under the Euclidean topology $\tau_d$.


Then $\struct {\R \setminus \Q, \tau_d}$ is paracompact.


Proof

From Euclidean Space is Complete Metric Space, a Euclidean space is a metric space.

The result follows from Metric Space is Paracompact.

$\blacksquare$


Sources