<p>It was demonstrated in [2] that the Alexandroff duplicate of Čech-Stone compactification naturals is not extremally disconnected. The question raised as to whether a non-discrete disconnected space can ever be We answer this affirmative; an example van Douwen significant. In slightly different direction we also characterize when P-space well it almost P-space.</p>

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

We prove that every continuum of weight ℵ 1 is a continuous image of thě Cech-Stone-remainder R * of the real line. It follows that under CH the remainder of the half line [0, ∞) is universal among the continua of weight c — universal in the 'mapping onto' sense. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R * , 2) in the ...

Let Γ be an infinite discrete group and βΓ its Čech-Stone compactification. Using the well known fact that a free ultrafilter on an infinite set is nonmeasurable, we show that for each element p of the remainder βΓ \ Γ, left multiplication Lp : βΓ → βΓ is not Borel measurable. Next assume that Γ is abelian. Let D ⊂ l(Γ) denote the subalgebra of distal functions on Γ and let D = Γ = |D| denote t...

The classic genetic algorithm has been successfully applied to many optimization problems. However, its usefulness is limited when it comes to feature selection, particularly if a high reduction rate is expected. The algorithm, in its classic version, returns feature sets containing approximately 50% of the total number of features. In order to decrease this rate, a penalty term penalizing indi...

Themain aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have gen...

This paper presents issues related to modeling and optimization of the feature generator for the speaker recognition system (ASR – Automatic Speakers Recognition). The parameterization stage of generating a speech signal (features generation) is fundamental in this type of system because the unique vector of features is crucial in the process of speech recognition. The task is to describe the s...

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in number ways, including as colimit homeomorphism groups with given compact support, or subgroup the its Stone-\v{C}ech compactification. A is said to have Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. authors provide necessary and sufficient conditions for finite produ...

The Royden ideal boundary of a domain is the set of all points in the maximal ideal space of the domain's Royden algebra that do not lie in the domain. Elements of the Royden ideal boundary can be characterized as nets convergent in both the weak and Euclidean topologies that have no subnet which is a sequence. As with other function algebras, boundary bers can be deened as subsets of all point...