Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

We use the insights of Robinson’s nonstandard analysis as a powerful tool to extend and simplify the construction of compactifications of regular spaces. In particular, we deal with the Stone-Čech compactification and compactifications formed from topological ends. For the nonstandard extension of a metric space, the monad of a standard point x is the set of all points infinitesimally close to ...

the main purpose of this paper is to establish a relation between universality of certain p-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. in particular, we show that if we take p to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, the...

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...