Witold Marciszewski

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We prove that if X is a countable nondiscrete completely regular space such that the function space C (X) is an absolute FaS-set, then C (X) is homeomorphic to <7°° , where a = {(x¡) e R00:*, = 0 for all but finitely many i} . As an application we answer in the negative some problems of A. V. Arhangel'skii by giving examples of countable completely regular(More)
1.1. The first term in the title of this essay, hypercomputational, requires elucidation as being quite a novelty (a bit shocking, perhaps) in the language of science. Fortunately, the term computational has a well-established meaning since Turing’s seminal study of 1936. Fortunately, as well, it was the same Turing, in his work of 1938, who offered us a(More)
An internal characterization of metric spaces which are absolute Borel sets of multiplicative classes is given. This characterization uses complete sequences of covers, a notion introduced by Froĺık for characterizing Čechcomplete spaces. We also show that the absolute Borel class of X is determined by the uniform structure of the space of continuous(More)
We announce a complete topological classification of the function spaces C (X) of Borel class not higher than 2, provided that I is a countable space. We also present a topological classification of the /c-dimensional universal pseudoboundaries and pseudointeriors in R , and we investigate under what conditions strong negligibility of crZ-sets characterizes(More)
We link here distances between iterated limits, oscillations, and distances to spaces of continuous functions. For a compact space K, a uniformly bounded set H of the space of real-valued continuous functions C(K), and ε ≥ 0, we say that H ε-interchanges limits with K, if the inequality |lim n lim m fm(xn) − lim m lim n fm(xn)| ≤ ε holds for any two(More)
1. Let us fancy for a moment that the first-order logic (FOL) is decidable. And let the famous Gödelian sentence (G) about its own unprovability, after its encoding in the language of arithmetic, be put as the consequent in the conditional whose antecedent is obtained as the conjunction of Peano axioms (P); thus we have: P ⇒ G — a sentence recorded in the(More)
For a completely regular space X, denote by Cp(X) the space of continuous real-valued functions on X, with the pointwise convergence topology. In this article we strengthen a theorem of O. Okunev concerning preservation of some topological properties of X under homeomorphisms of function spaces Cp(X). From this result we conclude new theorems similar to(More)