Electronic Resource
Springer
Annali di matematica pura ed applicata
31 (1950), S. 99-110
ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary One of the most useful results in introductory topology is the theorem that ifS is connected andC is a connected subset such thatS −C =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 & andS −P=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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02428259
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