Editing Open and closed maps (section)

==Notes==

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<ref name="DefOfRegularOpenClosed">A subset <math>S \subseteq X</math> is called a '''{{em|[[Regular closed set|{{visible anchor|regular closed set}}]]}}''' if <math>\overline{\operatorname{Int} S} = S</math> or equivalently, if <math>\operatorname{Bd} \left( \operatorname{Int} S \right) = \operatorname{Bd} S,</math> where <math>\operatorname{Bd} S</math> (resp. <math>\operatorname{Int} S,</math> <math>\overline{S}</math>) denotes the [[Boundary (topology)|topological boundary]] (resp. [[Interior (topology)|interior]], [[Closure (topology)|closure]]) of <math>S</math> in <math>X.</math> The set <math>S</math> is called a '''{{em|[[Regular open set|{{visible anchor|regular open set}}]]}}''' if <math>\operatorname{Int} \left( \overline{S} \right) = S</math> or equivalently, if <math>\operatorname{Bd} \left( \overline{S} \right) = \operatorname{Bd} S.</math> The interior (taken in <math>X</math>) of a closed subset of <math>X</math> is always a regular open subset of <math>X.</math> The closure (taken in <math>X</math>) of an open subset of <math>X</math> is always a regular closed subset of <math>X.</math></ref>
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