Projectively extended real line: Difference between revisions

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===Neighbourhoods===

Let <math>x \in \widehat{\mathbb{R}},</math> and <math>A \subseteq \widehat{\mathbb{R}}</math>.

*{{mvar|A}} is a [[Neighbourhood (mathematics)|neighbourhood]] of ''x'', if ''A'' contains an open interval ''B'' that contains {{mvar|x}}.

*{{mvar|A}} is a right-sided neighbourhood of {{mvar|x}}, if there is a real number {{mvar|y}} such that <math>y \neq x </math> and {{mvar|A}} contains the semi-open interval <math>[x, y)</math>.