Definition:Simplified Arens Square

Definition
Let $A$ be the set of points in the interior of the unit square:
 * $A := \set {\tuple {i, j}: 0 < i < 1, 0 < j < 1, i, j \in \R} = \openint 0 1^2$


 * Simplified-Arens-square.png

Let $S$ be the set defined as:


 * $S = A \cup \set {\tuple {0, 0} } \cup \set {\tuple {1, 0} }$

Let $\BB$ be the basis for a topology generated on $S$ be defined by granting:


 * to each point of $A$ the local basis of open sets inherited by $A$ from the Euclidean topology on the unit square;


 * to the other points of $S$ the following local bases:

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

$\struct {S, \tau}$ is referred to as the simplified Arens square.

Also see

 * Simplified Arens Square is Topology


 * Definition:Arens Square