Á. Császár

Generalized open sets in generalized topologies

SummaryWe study the even power means of a sum analogous to Dedekind sums, and give a sharp asymptotic formula.

On the γ-Interior and γ-Closure of a Set

For a set X, let γ : exp X → exp X satisfy γA ⊂ γB whenever A ⊂ B ⊂ X. In [4], γ-open subsets of X, γ-interior iγA and γ-closure cγA of A ⊂ X have been defined. The purpose of the present paper is to show that, under suitable conditions on γ, explicit formulas furnish iγA and cγA.

γ-Compact Spaces

Let X be a topological space, denote iA and cA the interior and the closure of A ⊂ X, respectively, and let γ = c o i, or = i o c, or = i o c o i, or = c o i o c. A set A ⊂ X is said to be γ-open [5] iff A ⊂ γ(A). The space X is γ-compact iff each cover of X composed of γ-open sets admits a finite subcover. The purpose of the paper is to investigate some questions concerning γ-compact and related spaces.

u-Isomorphic semigroups of continuous functions

0. Introduction. Let X be a topological space, and denote by C(X) the set of all real-valued continuous functions defined on X, by C*(X) the subset of C(X) composed of bounded functions. Both C(X) and C*(X) can be considered as a ring under pointwise addition and multiplication of functions, or as a semigroup under pointwise multiplication. For a completely regular Hausdorff space X, let f ix and vX denote the (~ech Stone compactification and the Hewitt realcompactification of X, respectively (see e. g. [2]). The following propositions are well-known for completely regular Hausdortf spaces X and Y:

On the Operation sup for Subcategories of mer

AbstractWe study properties of the operation

On a problem of simultaneous quasi-uniform extension

\sup

Transitive Quasi-Uniformities and Topogenous Orders

, defined for structures corresponding to different subcategories of MER, as merotopies, filter merotopies, contiguities,