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Displaying 1421 – 1440 of 1530

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On z◦ -ideals in C(X)

F. Azarpanah, O. Karamzadeh, A. Rezai Aliabad (1999)

Fundamenta Mathematicae

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,...

On α -continuous functions

Dragan S. Janković, Ch. Konstadilaki-Savvopoulou (1992)

Mathematica Bohemica

Classes of functions continuous in various senses, in particular θ -continuous, α -continuous, feeblz continuous a.o., and relations between the classes, are studied.

On α -normal and β -normal spaces

Aleksander V. Arhangel'skii, Lewis D. Ludwig (2001)

Commentationes Mathematicae Universitatis Carolinae

We define two natural normality type properties, α -normality and β -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 β -normal, pseudocompact space is countably compact, and show that if X is a dense subspace of a product of metrizable spaces, then X is normal if and only if X is β -normal. All hereditarily separable spaces are α -normal. A space is normal if and...

On β-favorability of the strong Choquet game

László Zsilinszky (2011)

Colloquium Mathematicae

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 W δ -subspace which is of the first category in itself.

On δ -continuous selections of small multifunctions and covering properties

Alessandro Fedeli, Jan Pelant (1991)

Commentationes Mathematicae Universitatis Carolinae

The spaces for which each δ -continuous function can be extended to a 2 δ -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.

On θ -closed sets and some forms of continuity

Mohammad Saleh (2004)

Archivum Mathematicum

In this paper, we further the study of θ -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using θ -open and δ -open sets. Among other results, it is shown a weakly θ -retract of a Hausdorff space X is a δ -closed subset of X .

Currently displaying 1421 – 1440 of 1530