Category:Pointed Rational Extension of Reals

This category contains results about Pointed Rational Extension of Reals.

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

Let $\Q$ denote the set of rational numbers.

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

$\BB = \set {\set x \cup \paren {U \cap \Q}: x \in U \in \tau_d}$

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

$\tau'$ is referred to as the pointed rational extension of $\R$.