Topological solutions in the (2+1)-dimensional Einstein theory of gravity are studied within the ADM canonical formalism. It is found that a conical singularity appears in the closed de Sitter universe solution as a topological defect in the case of the Einstein theory with a cosmological constant. Quantum effects on the conical singularity are studied using the de Broglie-Bohm interpretation. ...

A construction by Hofmann and Streicher gives an interpretation of a typetheoretic universe U in any Grothendieck topos, assuming a Grothendieck universe in set theory. Voevodsky asked what space U is interpreted as in Johnstone’s topological topos. We show that its topological reflection is indiscrete. We also offer a model-independent, intrinsic or synthetic, description of the topology of th...

We study issues of the quintessence in the brane cosmology. The initial bulk spacetime consists of two 5D topological anti de Sitter balck hole joined by the brane (moving domain wall). Here we do not introduce any conventional radiation and matter. Instead we include a localized scalar on the brane as a stress-energy tensor, and thus we find the quintessence which gives an accelerating univers...

We introduce the subcategory VRelR(H) of VRel(H) consisting of H-fuzzy reflexive relational space on sets and we study structures of VRelR(H) in a viewpoint of the topological universe introduced by L.D.Nel. We show that VRelPO(H) of VRelR(H). We show that VRelPR(H) [resp. VRelP (H) and VRelE(H)] is a topological universe over Set. Mathematics Subject Classification: 04A72, 18B10, 18D15

Abstract. This paper extends some essential topological properties in general topological spaces in to the I-rough topological spaces, the topology of the rough universe. I-rough compactness and I-rough Hausdorffness are introduced and several properties are investigated. I-rough compactness of subsets of I-rough Hausdorff spaces are studied. Also the paper establishes I-rough connectedness in ...

The Universe Type System is an ownership type system for object-oriented programming languages that hierarchically structures the object store; it is used to reason modularly about programs. We formalise Universe Types for a core subset of Java in two steps: We first define a Topological Type System that structures the object store hierarchically into an ownership tree, and demonstrate soundnes...

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

We investigate the global structure of inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early Universe. We show that the global structure of inflationary universe depends crucially on the mechanism of inflation. In the simplest models of chaotic inflation with the effective potentials φ or e the Universe looks like a sea of thermalized ...