Category:Definitions/Indiscrete Extensions of Reals
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This category contains definitions related to Indiscrete Extensions of Reals.
Related results can be found in Category:Indiscrete 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:
- $\BB := \set {H: \exists U \in \tau_d: H = U \cap D}$
Let $\tau^*$ be the topology generated from $\tau_d$ by the addition of all sets of $\BB$.
- $\tau^* = \tau_d \cup \BB$
$\tau^*$ is then referred to as an indiscrete extension of $\R$.
Pages in category "Definitions/Indiscrete Extensions of Reals"
The following 5 pages are in this category, out of 5 total.