Projectively extended real line: Difference between revisions

Revision as of 17:32, 3 April 2022

Revision as of 17:31, 4 April 2022

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*{{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>.

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

*{{mvar|A}} is a [[punctured neighbourhood]] (resp. a right-sided or a left-sided punctured neighbourhood) of {{mvar|x}}, if <math>x\not\in A,</math> and <math>A\cup\{x\}</math> is a neighbourhood (resp. a right-sided or a left-sided neighbourhood) of {{mvar|x}}.