Abstract
AbstractIn this article the study of OČAN spaces is continued. In a space 𝒫(𝒜, ℬ︁) some topological properties are not disturbed if 𝒜 and ℬ︁ 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 𝒫(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 𝒫(𝒜, ℬ︁) 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.
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