Assuming AD+DC(R), we characterize the self-dual boldface pointclasses which are strictly larger (in terms of cardinality) than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank ≤ ω 1, and those of Wadge rank < ω ξ 1 when ξ is limit.

A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...

In the current paper, a procedure for obtaining clopen topology from a general binary relations R via proximity structures was obtained. A comparison between the properties of approximation with respect to the topologies generated by relation and their corresponding approximation with respect to proximity structures were carried out.

A topological space X is called a CO space, if every closed subset of X is homeomorphic to some clopen subset of X. Every ordinal with its order topology is a CO space. This work gives a complete classification of CO spaces which are continuous images of compact ordered spaces. 1 AMS Subject Classification 2000: Primary 06E05. Secondary 54G12, 06A05

We study MB-representations of algebras and ideals when they are relativized to a subset, and when one considers the operations of sum and intersection for families of algebras and ideals. We observe that the algebras ∆α, 3 ≤ α < ω1, on R are MB-representable under GCH. We find a class of topological spaces in which the algebra of clopen sets is MB-representable.

Under the additional assumption of complete regularity, we furnish a simple characterization all topologies such that every continuous total preorder is representable by utility function. In particular, prove completely regular topology satisfies property if, and only it separable linearly ordered collection clopen sets countable. Since not restrictive to refer when dealing with this kind probl...

It is shown that the product of finitely many sequential, CLP-compact spaces is CLPcompact. The class of spaces which have the property that every cover by clopen sets — sets which are both open and closed — has a finite subcover was introduced by A. Šostak in [1] under the name CBcompact. These spaces are now known as CLP-compact spaces and their study is linked to the question of whether the ...

A flow on a compact Hausdorff space X is given by a map t : X → X. The general goal of this paper is to find the “cyclic parts” of such a flow. To do this, we approximate (X, t) by a flow on a Stone space (that is, a totally disconnected, compact Hausdorff space). Such a flow can be examined by analyzing the resulting flow on the Boolean algebra of clopen subsets, using the spectrum defined in ...

Powar P. L. and Rajak K., have introduced fine-topological space which is a special case of generalized topological sspace. In this paper, the author has introduced a new class of functions called fine weakly BR-continuous functions on fine topological space (cf. [12]). Weakly BR-continuous functions has been introduced by Ekici [3] which includes the class of strongly continuous functions due ...

Special thanks to my advisor Steffen Lempp for his guidance and conversation. Abstract Always Sometimes 2 In this talk I will present the necessary background and then describe and characterize the non-branching degrees. Significantly, I will show three distinct classes of non-branching degrees. The Medvedev lattice of Π 0 1 classes is a lattice of certain subsets of 2 ω under a natural reducti...