Annali di Matematica Pura ed Applicata

, Volume 31, Issue 1, pp 99–110 | Cite as

On a certain class of set theoretic properties

  • Paul A. White


One of the most useful results in introductory topology is the theorem that ifS is connected andC is a connected subset such thatSC =X∪Y, separate (« » means union), thenX∪C andY∪C are connected. In this paper a study is made of other set properties satisfying a similar theorem. That is, ifP ⊂ S both have a property & andSP=X∪Y separate, thenP∪X andP∪Y have this property. Furthermore, many properties have corresponding localizations, for example local connectedness, and it is determined under what conditions the corresponding local property satisfies the above theorem if the original property does.


Local Property Theoretic Property Connected Subset Original Property Local Connectedness 
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Copyright information

© Swets & Zeitlinger B. V. 1950

Authors and Affiliations

  • Paul A. White
    • 1
  1. 1.Los AngelesU. S. A.

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