Locally linearly S-closed spaces
Resumo
The purpose of the present paper is to study the class of locally linearly S-closed spaces. Characterizations and cardinality bounds for the class of locally linearly S-closed spaces are obtained. It is shown that weakly Lindel¨of, Hausdorff, lob and locally linearly S-closed spaces having (i) countable tightness are discrete spaces of countable cardinality; (ii) countable π-character and countable pseudocharacter are of cardinality at most 2ω. In addition, we provide some sufficient conditions for a locally linearly S-closed space to be extremally disconnected. It is shown that Hausdorff (or almost regular), lob, locally linearly S-closed spaces are extremally disconnected. Moreover, it turns out that maximal locally linearly S-closed spaces are also extremally disconnected. Some conditions on functions that preserve (inversely preserve) the property of being locally linearly S-closed are also investigated.
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