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Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

The Sorgenfrey linePolka Sleeve Cap Blue Swing Dot Women Navy Retro Party 1950s Vintage Midi Dress fxW1g1PwnI (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 [Cheetah Size INC International Concepts Macy's Print Created I C for Plus N Animal Blouse a,Macy's for Blouse N I Concepts Plus Created INC Size Cheetah Print C International Animal b). This is sometimes called the lower limit topology?, and the Sorgenfrey line is often denoted by l.

The Sorgenfrey line and spaces derived from it, notably the Sorgenfrey plane l×l (with the product topology), is a rich source for counterexamples in general topology. For example, the Sorgenfrey line is a (T1) 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.

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