Category:Discrete Irrational Extension of Reals

This category contains results about Discrete Irrational Extension of Reals.

Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.

Let $\Bbb I := \R \setminus \Q$ denote the set of irrational numbers.

Let $\BB$ be the set of sets defined as:

$\BB = \tau_d \cup \set {\set x: x \in \Bbb I}$

Let $\tau*$ be the topology generated from $\BB$.

$\tau^*$ is referred to as the discrete irrational extension of $\R$.