The purpose of this initial chapter is to clarify our peculiarities of notation and meaning. Our terminology from general topology will usually coincide with that of a standard text such as Kelley  with the following exceptions. A compact space is a space that has the finite subcover property and is Hausdorff. Thus a locally compact space will always be Hausdorff. In addition, a normal space is one in which disjoint closed sets can be separated by disjoint open neighborhoods and is Hausdorff. Thus a normal space for us is what Kelley would call T4. This also applies to perfect normality.
KeywordsDisjoint Union Compact Space Deformation Retract Deformation Retraction Strong Deformation Retract
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