Definition:Sorgenfrey's Half-Open Square Topology

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Let $A = \struct {\R, \sigma}$ be a Sorgenfrey line.

Let $S = A \times A$ denote the product space of $A$ with itself, whose topology $\tau$ is such that:

the neighborhood of a point $\tuple {p, q}$ is a rectangle in $\R^2$ of the form:
$\set {\set {x, y}: p \le x < p + \epsilon_1, q \le y < q + \epsilon_2}$
for some $\epsilon_1, \epsilon_2 \in \R_{>0}$.

$\struct {S, \tau}$ is referred to as Sorgenfrey's half-open square topology.

Also see

  • Results about Sorgenfrey's half-open square topology can be found here.

Source of Name

This entry was named for Robert Henry Sorgenfrey.