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ON SPACES IN WHICH COMPACT-LIKE SETS ARE CLOSED, AND RELATED SPACES
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 Title & Authors
ON SPACES IN WHICH COMPACT-LIKE SETS ARE CLOSED, AND RELATED SPACES
Hong, Woo-Chorl;
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 Abstract
In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is -Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits , and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.
 Keywords
KC;C-closed;SC-closed;-Urysohn;sequential;AP;WAP;weakly discretely generated;
 Language
English
 Cited by
1.
ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT,;

대한수학회논문집, 2010. vol.25. 3, pp.477-484 crossref(new window)
2.
A GENERALIZATION OF A SEQUENTIAL SPACE AND RELATED SPACES,;;

호남수학학술지, 2014. vol.36. 2, pp.425-434 crossref(new window)
1.
A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS, East Asian mathematical journal, 2016, 32, 3, 365  crossref(new windwow)
2.
ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT, Communications of the Korean Mathematical Society, 2010, 25, 3, 477  crossref(new windwow)
3.
A GENERALIZATION OF A SEQUENTIAL SPACE AND RELATED SPACES, Honam Mathematical Journal, 2014, 36, 2, 425  crossref(new windwow)
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