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The generalized Očan topology on sets of subsets and topological Boolean rings
Author(s) -
Kašuba R.
Publication year - 1980
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19800970106
Subject(s) - mathematics , disjoint sets , topological space , space (punctuation) , simple (philosophy) , topology (electrical circuits) , plane (geometry) , pure mathematics , totally disconnected space , locally compact space , discrete mathematics , combinatorics , geometry , philosophy , linguistics , epistemology
In this article the study of OČAN spaces is continued. In a space (, ℬ) some topological properties are not disturbed if and ℬ are enlarged. The SORGENFREY plane can be identified with some OČAN space (Example 1). By use of systems of almost disjoint subsets some special topological rings on ( X ) can be constructed (Propositions 8 and 9). A metrisable or a locally compact OČAN ring has a simple structure (Propositions 10 and 11). If (, ℬ) neither discrete nor compact, then the closedness of all simple maps is a very strong condition (Theorem 1). The space of VIETORIS is in general not σ‐extremally disconnected space (Theorem 2). At the end of the article some generalizations are made and some bibliographical references are given.