The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

Topological defects are produced during phase transitions in the very early Universe. They arise in most unified theories of strong, weak and electromagnetic interactions. These lectures focus on the role of topological defects in cosmology, with particular emphasis on the models of structure formation based on defects. The role of topological defects in baryogenesis is also reviewed. ⋆ Based o...

We introduce the consistent topological structure and neighborhood structure into the logical framework for providing the logical foundation and logical normalization for the approximate reasoning. We present the concept of the formulae mass, theknowledge mass and the approximating knowledge closure of the knowledge library by means of topological closure. We obtain the fundamental framework of...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

47 thereby facilitating reduction of polyoxometallates of these types. The concept of binodal orbital aromaticity in reduced early-transition-metal polyoxometallates may be related to their classification as mixed valence compounds. Robin and Day36 classify mixed valence compounds into the following three classes: Class I, fully localized corresponding to an insulator in an infinite system; Cla...

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 ...

We investigate the null geodesic flow and in particular light rings (LRs), fundamental photon orbits (FPOs) shadows of a black hole (BH) immersed strong, uniform magnetic field, described by Schwarzschilld-Melvin electrovacuum solution. The empty Melvin Universe contains tube planar LRs. Including BH, for weak fields, shadow becomes oblate, whereas intrinsic horizon geometry prolate. For strong...

In running mass inflation and hybrid inflation models it is possible that the inflaton field will fragment into non-topological solitons, resulting in a highly inhomogeneous post-inflation era prior to reheating. In supersymmetric models with a conventional homogeneous post-inflation era, the dynamics of flat direction scalars are determined by cH corrections to the mass squared terms (where |c...