In this paper we define gradation of RS-compactness and S*-closed spaces in L-topological spaces.We generalize the degrizations of RS-compactness and S*-closedness to the L-topological space and give the positions of them under weak forms of L-continuity. 2010 AMS Classification: 54A40, 06D72

Kuratowski [6] showed that a continuous compact map f : X → X defined on a closed convex subset X of a Banach space has a fixed point. This theorem has enormous influence on fixed point theory, variational inequalities, and equilibrium problems. In 1968, Goebel [5] established the well-known coincidence theorem, and then there had been a lot of generalization and application (see, [1, 2, 5]). L...

Let K be a compact Hausdorff space and let )~ be a probability measure on K. We denote by Lo(K,2) the space of all Borel functions f:K--*N with the topology of convergence in measure. Lo(K, 2) is an F-space (complete metric topological vector space) if, as usual, we identify functions equal almost everywhere. Spaces of the type Lo(K,2 ) are probably the most studied examples of non-locally conv...

Vector fields defined only over a part of a manifold give rise to indexes and to transfers. These local vector fields form a topological space whose relation to configuration spaces was studied by Dusa McDuff, and whose higher dimensional homotopy and homology promise invariants of parametrized families of local vector fields. We show that the assignment of the transfer to the vector field give...

We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein gravity to restore the large symmetry of its topological version. The wave function of the universe is obtained for each model. † Talk given at the Workshop ...

Sunada’s work on topological crystallography emphasizes the role of the ‘maximal abelian cover’ of a graph X. This is a covering space of X for which the group of deck transformations is the first homology group H1(X,Z). An embedding of the maximal abelian cover in a vector space can serve as the pattern for a crystal: atoms are located at the vertices, while bonds lie on the edges. We prove th...