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### Context

#### Topology

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

The Sorgenfrey lineShort Casual J Dress Crew Silk xzqnw07Rg (after Robert Sorgenfrey?, a mathematical descendant of R.L. Moore?) is the real line , but topologized by taking as topological basis the collection of half-open intervals . This is sometimes called the lower limit topology?, and the Sorgenfrey line is often denoted by .

The Sorgenfrey line and spaces derived from it, notably the Sorgenfrey plane (with the product topology), is a rich source for counterexamples in general topology. For example, the Sorgenfrey line is a () Black fit neck slim jumper V FPq1nF and even a paracompact space, but the Sorgenfrey plane fails to be normal (and thus is not paracompact either). The Sorgenfrey plane is also an example of a separable space, but admitting an uncountable discrete subspace (which is thus not separable), showing that separability is not a hereditary property.

Last revised on May 22, 2017 at 15:20:01. See the history of this page for a list of all contributions to it.

• #### Product Details

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