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An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals. Finally,...
Improving the recent result of the author we show that is equivalent to for every subgroup of a Hausdorff locally compact group .
Classes of functions continuous in various senses, in particular -continuous, -continuous, feeblz continuous a.o., and relations between the classes, are studied.
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
We define two natural normality type properties, -normality and -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every -normal, pseudocompact space is countably compact, and show that if is a dense subspace of a product of metrizable spaces, then is normal if and only if is -normal. All hereditarily separable spaces are -normal. A space is normal if and...
In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty -subspace which is of the first category in itself.
The spaces for which each -continuous function can be extended to a -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.
In this paper, we further the study of -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using -open and -open sets. Among other results, it is shown a weakly -retract of a Hausdorff space is a -closed subset of .
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