Category:Discrete Extensions of Reals
Jump to navigation
Jump to search
This category contains results about Discrete Extensions of Reals.
Definitions specific to this category can be found in Definitions/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 $\R$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
D
- Discrete Rational Extension of Reals (empty)