On the complexity of computable real sequences
On the complexity of events recognizable in real time
On the complexity of H sets of the unit circle
On the complexity of subspaces of
Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel’skiĭ-Franklin space is . In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of . We show that has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology. Moreover,...
On the complexity of sums of Dirichlet measures
Let be the set of all Dirichlet measures on the unit circle. We prove that is a non Borel analytic set for the weak* topology and that is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates from (or even , the set of all measures singular with respect to every measure in . This extends results of Kaufman, Kechris and Lyons about and and gives many examples of non Borel analytic sets.
On the complexity of the word problem for finitely presented commutative semigroups.
On the concreteness of quantum logics
It is shown that for any quantum logic one can find a concrete logic and a surjective homomorphism from onto such that maps the centre of onto the centre of . Moreover, one can ensure that each finite set of compatible elements in is the image of a compatible subset of . This result is “best possible” - let a logic be the homomorphic image of a concrete logic under a homomorphism such that, if is a finite subset of the pre-image of a compatible subset of , then is compatible....
On the congruence lattice of stable algebras with definability of compact congruences
On the congruences in four-valued modal algebras
On the Conjugacy Problem for Knot Groups.
On the consistency of the generalized continuum hypothesis.
On the consistency of the generalized continuum hypothesis [Book]
On the construction of dense lattices with a given automorphisms group
We consider the problem of constructing dense lattices in with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions , we exhibit a finite set of lattices that come with an automorphisms group of size , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...
On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices
Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the...
On the constructions of t-norms and t-conorms on some special classes of bounded lattices
Recently, the topic related to the construction of triangular norms and triangular conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an appropriate bounded lattice. Also, we give some illustrative examples for clarity. Then, we show that a new construction method can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on...
On the Continuity of Internal Functions
On the continuity set of an Omega rational function
In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore...
On the Convenient Setting for Real Analytic Mappings.
On the convergence and absolute continuity of signed states on a logic
On the Converse of Caristi's Fixed Point Theorem
Let X be a nonempty set of cardinality at most and T be a selfmap of X. Our main theorem says that if each periodic point of T is a fixed point under T, and T has a fixed point, then there exist a metric d on X and a lower semicontinuous map ϕ :X→ ℝ ₊ such that d(x,Tx) ≤ ϕ(x) - ϕ(Tx) for all x∈ X, and (X,d) is separable. Assuming CH (the Continuum Hypothesis), we deduce that (X,d) is compact.