Abstract We investigate the computability (in sense of computable analysis) topological pressure P top ( ϕ ) on compact shift spaces X for continuous potentials ϕ : X → <mml:mi mathvariant="double-struc...

Let (rI , r, ,...) be a sequence of non-negative integers summing to n. We determine under what conditions there exists a finite distributive lattice L of rank n with ri join-irreducibles of rank i, for all i = 1,2,.. . . When I. exists, we give explicit expressions for the greatest number of elements L can have of any given rank, and for the greatest total number of elements L can have. The pr...

We define a topological space for the complexes of fixed dimension vector over the derived category of a finite dimensional algebra with finite global dimension. It has a local structure of affine variety under the action of the algebraic group. We consider the constructible functions which reflect the stratifications of the orbit spaces. By using the convolution rule, we obtain the geometric r...

Compact fuzzy topological spaces were first introduced by Chang [3]. o-compact fuzzy topological spaces were introduced by Gantner et al. [4]. Abd El-Monsef et al. [1] introduced the notion of e-aimost compact fuzzy topological spaces. Mashhour et al. [8] introduced the notion of bifuzzy topological spaces and defined the notion of o-compactness in those spaces. In this paper, we obtain some ne...

Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for T1 spaces was already solved by G. E. Strecker in 1966. For certain topologies on hyperspaces (which are not necessarily T1), the main question was in the positive answered by Bruce S. B...

In this paper F1 denotes a non empty finite topology space and A, B, C denote subsets of F1. Let us consider F1. One can check that ∅(F1) is connected. We now state two propositions: (1) For all subsets A, B of F1 holds (A ∪ B) b = A ∪ B. (2) (∅(F1)) b = ∅. Let us consider F1. Observe that (∅(F1)) b is empty. Next we state the proposition (3) Let A be a subset of F1. Suppose that for all subset...

Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of ‘continuous functions’ which turn out to be noncomm...

In this paper we first study the moduli spaces related to Calabi-Yau manifolds. We then apply the results to the following problem. Let C be a fixed Riemann surface with fixed finite number of points on it. Given a CY manifold with fixed topological type, we consider the set of all families of CY manifolds of the fixed topological type over C with degenerate fibres over the fixed points up to i...