In this paper, we defined two new games - the mildly Menger game and compact-clopen game. a zero-dimensional space, is equivalent to compact-open An example given for space on which undetermined. Also introduced namely K-quasi-component-clopen proved that Then if topological union of countably many quasi-components compact sets, then TWO has winning strategy in

Let M and N be complex unital Jordan-Banach algebras, let M−1 N−1 denote the sets of invertible elements in N, respectively. Suppose that M⊆M−1 N⊆N−1 are clopen subsets N−1, respectively, which closed for powers, inverses products form Ua(b). In this paper we prove each surjective isometry Δ:M→N there exists a real-linear T0:M→N an element u0 McCrimmon radical such Δ(a)=T0(a)+u0 all a∈M. Assumi...

We show that for a discrete semigroup S there exists a uniquely determined complete Boolean algebra B(S) the algebra of clopen subsets of M(S). M(S) is the phase space of the universal minimal dynamical system for S and it is an extremally disconnected compact Hausdorff space. We deal with this connection of semigroups and complete Boolean algebras focusing on structural properties of these alg...

Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that A' is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets. Then it is proved that each countable Boolean algebra has the corresponding property. As a corollary ...

A continuous function f with domain X and range f(X) in R n is weakly univalent if there is a sequence of continuous one-to-one functions on X converging to f uniformly on bounded subsets of X. In this article, we establish, under certain conditions, the connectedness of an inverse image f ?1 (q). The univalence results of Radulescu-Radulescu, Mor e-Rheinboldt, and Gale-Nikaido follow from our ...

Let G be a finite connected graph, and let ∆ be its universal covering tree. The edges of ∆ are directed and each geometric edge corresponds to two directed edges δ and δ. Let ∆ be the set of vertices and ∆ the set of directed edges of ∆. The boundary ∂∆ is the set of equivalence classes of infinite semi-geodesics in ∆, where two semi-geodesics are equivalent if they agree except on finitely ma...

We show how to deene domains of processes, which arise in the denotational semantics of concurrent languages, using hypersets, i.e. non-wellfounded sets. In particular we discuss how to solve recursive equations involving set-theoretic operators within hyperuniverses with atoms. Hyperuniverses are transitive sets which carry a uniform topo-logical structure and include as a clopen subset their ...

For almost finite groupoids, we study how their homology groups reflect dynamical properties of their topological full groups. It is shown that two clopen subsets of the unit space has the same class in H0 if and only if there exists an element in the topological full group which maps one to the other. It is also shown that a natural homomorphism, called the index map, from the topological full...

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.