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

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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...