Category:Definitions/Discrete Extensions of Reals

This category contains definitions related to Discrete Extensions of Reals.
Related results can be found in Category:Discrete Extensions of Reals.

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

Let $D$ be an everywhere dense subset of $\struct {\R, \tau_d}$ with an everywhere dense complement in $\R$.

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

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

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

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