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Dichotomies pour les espaces de suites réelles

Pierre Casevitz (2000)

Fundamenta Mathematicae

There is a general conjecture, the dichotomy (C) about Borel equivalence relations E: (i) E is Borel reducible to the equivalence relation E G X where X is a Polish space, and a Polish group acting continuously on X; or (ii) a canonical relation E 1 is Borel reducible to E. (C) is only proved for special cases as in [So].  In this paper we make a contribution to the study of (C): a stronger conjecture is true for hereditary subspaces of the Polish space ℝ ω of real sequences, i.e., subspaces such that [ y = ( y n ) n ∈ X ...

Difference functions of periodic measurable functions

Tamás Keleti (1998)

Fundamenta Mathematicae

We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions Δ h f ( x ) = f ( x + h ) - f ( x ) are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, ℌ ( ℱ , G ) = H ⊂ ℝ / ℤ : ( ∃ f ∈ ℱ G ) ( ∀ h ∈ H ) Δ h f ∈ G , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group 𝕋 = ℝ / ℤ that are invariant for changes on null-sets (e.g. measurable...

Dimensional compactness in biequivalence vector spaces

J. Náter, P. Pulmann, Pavol Zlatoš (1992)

Commentationes Mathematicae Universitatis Carolinae

The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a π -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set s and classes of set functions s → Q ...

Disasters in metric topology without choice

Eleftherios Tachtsis (2002)

Commentationes Mathematicae Universitatis Carolinae

We show that it is consistent with ZF that there is a dense-in-itself compact metric space ( X , d ) which has the countable chain condition (ccc), but X is neither separable nor second countable. It is also shown that X has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply the disjoint union of metrizable spaces is normal.

Discussion of the structure of uninorms

Paweł Drygaś (2005)

Kybernetika

The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing...

Disjointness of fuzzy coalitions

Milan Mareš, Milan Vlach (2008)

Kybernetika

The cooperative games with fuzzy coalitions in which some players act in a coalition only with a fraction of their total “power” (endeavor, investments, material, etc.) or in which they can distribute their “power” in more coalitions, are connected with some formal or interpretational problems. Some of these problems can be avoided if we interpret each fuzzy coalition as a fuzzy class of crisp coalitions, as shown by Mareš and Vlach in [9,10,11]. The relation between this model of fuzziness and...

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