Dimension theory and fuzzy topological spaces.
Dimensional compactness in biequivalence vector spaces
The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a -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 and classes of set functions ...
Diophantine geometry over groups I : Makanin-Razborov diagrams
This paper is the first in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the first paper we present the (canonical) Makanin-Razborov diagram that encodes the set of solutions of a system of equations. We continue by studying parametric families of sets of solutions, and associate with such a family a canonical graded Makanin-Razborov diagram, that encodes the collection...
Diophantine representation of Mersenne and Fermat primes
Diophantine undecidability for addition and divisibility in polynomial rings
We prove that the positive-existential theory of addition and divisibility in a ring of polynomials in two variables A[t₁,t₂] over an integral domain A is undecidable and that the universal-existential theory of A[t₁] is undecidable.
Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0
Let be a one-variable function field over a field of constants of characteristic 0. Let be a holomorphy subring of , not equal to . We prove the following undecidability results for : if is recursive, then Hilbert’s Tenth Problem is undecidable in . In general, there exist such that there is no algorithm to tell whether a polynomial equation with coefficients in has solutions in .
Direct decomposability of tolerances and congruences on semigroups
Direct multiples and powers of modules
Direct product decomposition of -algebras
Direct product decompositions of bounded commutative residuated -monoids
The notion of bounded commutative residuated -monoid (-monoid, in short) generalizes both the notions of -algebra and of -algebra. Let be a -monoid; we denote by the underlying lattice of . In the present paper we show that each direct...
Directoids with sectionally antitone involutions and skew MV-algebras
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
Directoids with sectionally switching involutions
It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.
Dirichlet theorems and prime number hypotheses of a conditional Goldbach theorem.
Disasters in metric topology without choice
We show that it is consistent with ZF that there is a dense-in-itself compact metric space which has the countable chain condition (ccc), but is neither separable nor second countable. It is also shown that 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.
Disconnectedness of Sublevel Sets of Some Riemannian.
Discontinuous homomorphisms from C(K)
Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up
Discriminator varieties of Boolean algebras with residuated operators
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated...
Discussion of the structure of uninorms
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...
Disjoint refinement and related topics