In this paper we study the topological directional entropy of 2  -actions by generated linear cellular automata (CA hereafter), defined by a local rule f[l,r], l, r , l  r, i.e. the maps Tf[l, r]: m m      which are given by Tf[l, r](x) = ( ) n n y   , yn = f(xn+l, ..., xn+r) = r x i n i i l     (mod m), x=    n n x ) (  m   and f: 1 r l m     Zm, over the ring Zm (m...

Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in mani...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

Various aspects of super-space topology and N=l supersymmetry in 2+1 dimensions are explored. Non-Minimal super Yang-Mills theory is used to construct a gauge theory of the N=l super-Poincare’ algebra. A topological super Yang-Mills theory is given and used to compute elements of the cohomology classes of super-monopole moduli space. Submitted to Nuclear Physics B t This work is supported by th...

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...

Abstract The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is very well behaved analogue differential in the context topological spaces, satisfying good properties such as existence resolutions singularities handlebody decompositions. In this paper we prove Tanaka’s conjecture that any Whitney admits canonical structure. We thus est...

Let A be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space A[τ ]. Then A is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several c...

In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarl...

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...