We construct two Borel equivalence relations on the generalized Baire space κ, κ = κ > ω, with the property that neither of them is Borel reducible to the other. A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy fails. By λ we denote the set of all functions κ→ λ. We define a topology to (λ) by letting the sets N(η1...,ηn) = {(f...

In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that  right and product stabilizers are filters and if they are ...

We investigate the relationship between the synthetic approach to topology, in which every set is equipped with an intrinsic topology, and constructive theory of metric spaces. We relate the synthetic notion of compactness of Cantor space to Brouwer’s Fan Principle. We show that the intrinsic and metric topologies of complete separable metric spaces coincide if they do so for Baire space. In Ru...

Two classes of spaces are studied, namely locally realcompact spaces and HNcomplete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences ...

We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. Theorem. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. Theorem. In the Ellentuck topology on [ω] , (s)0 is a proper subset of the...

Computable analysis provides ways of representing points in a topological space, and therefore defining notion computable the space. In this article, we investigate when two topologies on same space induce different sets points. We first study purely version problem, which is to understand are not -homeomorphic. obtain characterization leading an effective version, prove that satisfying conditi...

We consider the typical behaviour of random dynamical systems order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at endpoints. Our study removes any requirement for continuous differentiability save existence finite derivatives endpoints interval. construct suitable Baire space structure this class systems. Generically within our space, we show that stationary ...

In this paper, the concepts of pairwise fuzzy Baire bitopological spaces are introduced and characterizations of pairwise fuzzy Baire bitopological spaces are studied. Several examples are given to illustrate the concepts introduced in this paper.

We study the functions whose composition with Baire class one functions are Baire class one functions. We first prove some characterizations of such functions, then investigate a subclass of such functions which are defined in a natural way.