in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...

Perhaps the most strikingly counterintuitive theorem in mathematics is the "Banach-Tarski paradox": A ball in R3 can be decomposed into finitely many pieces which can be rearranged by rigid motions and reassembled to form two balls of the same size as the original. The Axiom of Choice is used to construct the decomposition; the "paradox" is resolved by noting that the pieces cannot be Lebesgue ...

For [Formula: see text], the coarse similarity class of denoted by is set all text] such that symmetric difference and has asymptotic density text]. There a natural metric on space classes defined letting be upper We study under this metric, show in particular between any two distinct points there are continuum many geodesic paths. also subspaces form where closed Turing equivalence, tight conn...

This result is also due independently to G. Hector [3], who has shown how useful it can be in understanding the geometry of certain foliated manifolds. In such applications one sometimes needs a form of this theorem which applies to foliated subspaces, for example a minimal subset of a foliation. In fact our proof goes through unaltered in the situation where M is a locally compact, paracompact...

There is a natural topology on the symmetric group on an infinite set Ω . If Ω is countable , the topology is derived from a metric , and the group is complete . This paper gives an account of this topology , including translations of topological concepts for permutation groups , the use of Baire category and Haar measure , and some results about confinitary permutation groups which are motivat...

Classically it is known that any set with packing dimension less than 1 is meager in the sense of Baire category. We establish a resource-bounded extension: if a class X has ∆-strong dimension less than 1, then X is ∆-meager. This has the applications of explaining some of Lutz’s simultaneous ∆-meager, ∆-measure 0 results and providing a new proof of a Gu’s strong dimension result on infinitely...

Using a game-theoretic characterization of Baire spaces, conditions upon the domain and the range are given to ensure a "fat" set C(f) of points of continuity in the sets of type X x {/}, y E Y for certain almost separately continuous functions f X Y Z These results (especially Theorem B) generalize Mibu’s First Theorem, previous theorems of the author, answers one of his problems as well as th...

We show that any symmetric, Baire measurable function from the complement of E0 to a finite set is constant on an E0-nonsmooth square. A simultaneous generalization of Galvin’s theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on E0-nonsmooth sets, this result is proved by relating E0-nonsmooth sets to ...