In classical homotopy theory, the homotopy hypothesis asserts that the fundamental ω-groupoid construction induces an equivalence between topological spaces and weak ω-groupoids. In the light of Voevodsky’s univalent foundations program, which puts forward an interpretation of types as topological spaces, we consider the question of transposing the homotopy hypothesis to type theory. Indeed suc...

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

We have measured the optical conductivity σ(ω) of the mixed-valent compound YbAl3. σ(ω) exhibits a mid-infrared peak centered at 0.150.2 eV, which becomes more pronounced with decreasing temperature (T ). In addition, a strong depletion of the spectral weight, i.e., a pseudogap formation, is observed in σ(ω) below ∼ 0.1 eV. A comparison of σ(ω) with the dc conductivity indicates the existence o...

We study theoretically the cooperative light emission from a system of N ≫ 1 classical oscillators confined within a volume with spatial scale, L, much smaller than the radiation wavelength, λ0 = 2πc/ω0. We assume that the oscillators frequencies are randomly distributed around a central frequency, ω0, with some characteristic width, Ω ≪ ω0. In the absence of disorder, that is Ω = 0, the cooper...

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density, connectedness, genericity) of these groups and their subgroups are studied. In this paper, we intend to present a unified approach to the study of topological properties of transformation groups in ergodic theory, Bo...

Let Ω be a connected compact Hausdorff space and X a Banach space for which the strong Banach-Stone property is valid. We give a complete characterization of the generalized bi-circular projection on the Banach spaces C(Ω) and C(Ω, X). We show that in each case generalized bi-circular projections are bi-contractive. We also give some results concerning projections in the convex hull of two or m...

An example is given of a plane topological torsion defect representing a cosmic wall double wall in teleparallel gravity.The parallel planar walls undergone a repulsive gravitational force due to Cartan torsion.This is the first example of a non-Riemannian double cosmic wall.It is shown that the walls oscillate with a speed that depends on torsion and on the surface density of the wall.Cartan t...