Category:Pointed Extensions of Reals
Jump to navigation
Jump to search
This category contains results about Pointed Extensions of Reals.
Definitions specific to this category can be found in Definitions/Pointed 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:
- $\BB = \set {\set x \cup \paren {U \cap D}: x \in U \in \tau_d}$
Let $\tau'$ be the topology generated from $\BB$.
$\tau'$ is referred to as a pointed extension of $\R$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
P
- Pointed Rational Extension of Reals (empty)