The measurements of CMB anisotropy have opened up a window for probing the global topol-ogy of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in models with nontrivial topol-ogy and apply it to open universe models with compact spatial topology. We conduct a Bayesian probability analysis for a selection...

Following the introduction of fuzzy sets in 1965, a notion of fuzzy topological group was proposed by Foster in 1979: essentially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of fuzzy topological group was introduced by Ma and Yu in 1984 by replacing points by fuzzy points. Recently two of the coauthors have introduced the notion of the topology indu...

We present a new Lorentz gauge invariant U(1) topological field theory in Riemann-Cartan spacetime manifold U4. By virtue of the decomposition theory of U(1) gauge potential and the φ–mapping topological current theory, it is proved that the U(1) complex scalar field φ(x) can be looked upon as the order parameter field in our Universe, and the set of zero points of φ(x) create the cosmic string...

In this paper we focus on the first condition. Non-perturbative electroweak baryogenesis offers the intriguing possibility that topological features of the Standard Model might be (in part) responsible for baryon and lepton number violation in the early Universe [2, 3, 4, 5]. In this talk we argue that electroweak baryogenesis in the early Universe is accompanied by the formation of a “topologi...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

We study some topological aspects of non-abelian gauge theories intimately connected to the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection to the non-perturbative solution to strong CP problem as originally proposed by the author is also discussed. Some relevant topological formulas are also given and discussed. A result fro...