Projectively extended real line: Difference between revisions

Revision as of 16:06, 3 April 2022

Revision as of 17:04, 3 April 2022

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*''A'' is a right-sided neighbourhood of x, if and only if there is <math>y \in \widehat{\mathbb{R}}\setminus \{x\}</math> such that ''A'' contains <math>[x, y)</math>.

*''A'' is a left-sided neighbourhood of x, if and only if there is <math>y \in \widehat{\mathbb{R}}\setminus \{x\}</math> such that ''A'' contains <math>(y, x]</math>.

*''A'' is a (right-sided, left-sided) [[Neighbourhood (mathematics)#Deleted neighbourhood|punctured neighbourhood]] of ''x'', if and only if there is <math>B \subseteq \widehat{\mathbb{R}}</math> such that ''B'' is a (right-sided, left-sided) neighbourhood of x, and <math>A = B \setminus \{x\}</math>.

===Limits===