Basic topological constructions of manifold stratified spaces and stratified approximate fibrations are studied. These include products of manifold stratified spaces, products and compositions of stratified approximate fibrations and Euclidean stabilization of stratified approximate fibrations. The main result shows that the adjunction of two manifold stratified spaces via a manifold stratified...

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

The replacement problem for stratified spaces asks whether any manifold (simple) homotopy equivalent to the bottom stratum of a stratified space X is the bottom stratum of a stratified space stratified (simple) homotopy equivalent to X. This is impossible in general, as one sees by considering X = M × [0, 1] and working rel M ×0. On the other hand, the classic theorem of Browder, Casson, Haefli...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

We introduce a notion of topological quandle. Given a topological quandle Q we associate to every classical link L in R an invariant JQ(L) which is a topological space (defined up to a homeomorphism). The space JQ(L) can be interpreted as a space of colourings of a diagram of the link L with colours from the quandle Q.

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

For any smooth free action of the unit circle S in a manifold M ; the Gysin sequence of M is a long exact sequence relating the DeRham cohomologies of M and its orbit space M/S. If the action is not free then M/S is not a manifold but a stratified pseudomanifold and there is a Gysin sequence relating the DeRham cohomology of M with the intersection cohomology of M/S. In this work we extend the ...