In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

In this note we introduce an action of the module of cyclohedra on the free loop space. We will then discuss how this action can be used in an appropriate recognition principle in the same manner as the action of Stasheff’s associahedra can be used to recognize based loop spaces. We will also interpret one result of R.L. Cohen as an approximation theorem, in the spirit of Beck and May, for free...

We obtain some topological results of the sequence spaces ∆m(X), where ∆m(X) = {x = (xk) : (∆xk) ∈ X}, (m ∈ N), and X is any sequence space. We compute the pα-, pβ-, and pγ-duals of l∞,c, and c0 and we investigate the N-(or null) dual of the sequence spaces ∆m(l∞),∆m(c), and ∆(c0). Also we show that any matrix map from ∆m(l∞) into a BK-space which does not contain any subspace isomorphic to ∆m(...

Let (X, ω) be a symplectic manifold, J be an ω-tame almost complex structure, and L be a Lagrangian submanifold. The stable compactification of the moduli space of parametrized J-holomorphic curves in X with boundary in L (with prescribed topological data) is compact and Hausdorff in Gromov’s C∞-topology. We construct a Kuranishi structure with corners in the sense of Fukaya and Ono. This Kuran...

The aim of this paper is to introduce the concept of fuzzy generalized closed set and study its properties. Secondly the concept of infra L-fuzzy topological space is introduced. Making use of fuzzy -closed sets and fuzzy -generalized closed sets the concept of fuzzy -generalized continuous mapping is introduced. Lastly the concept of fuzzy generalized closed irresolute map in L-fuzzy topologic...

: -We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. The case of the SO(2,l) group is separately discussed. A topological field theory is linked to the moduli space of “se...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

The observed strong dark-to-luminous matter coupling is described by a bias relation between visible and dark matter sources. We discuss the bias which emerges in the case where the topological structure of the Universe at very large distances does not match properly that of the Friedman space. With the use of such ”topological” bias, we construct the Universal Rotation Curve (URC) for spirals ...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

Eulerian poset is a basic and widely used combinatorial concept. It is the combinatorial version of manifolds and has the analogue of the Poincaré duality in the form of the DehnSommerville equations (linear relations among f -vectors). The concept has always been defined in the combinatorial language. As a topologist, my main insight is that a poset is Eulerian if and only if its underlying po...