Displaying similar documents to “To the isotropic generalization of Wallace lines.”

Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane

Adam St. Arnaud, Piotr Rudnicki (2013)

Formalized Mathematics


We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey...