Related papers: From A-spaces to arbitrary spaces via spatial fibr…
The aim of this work is to study the first order Dirac-Sobolev spaces in $L^p$ norm on an open subset of ${\mathbb R}^3$ to clarify its relationship with the corresponding Sobolev spaces. It is shown that for $1< p <\infty$, they coincide,…
In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
We prove that every group can be realized as the homeomorphism group and as the group of (pointed) homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homotopy-equivalent Alexandroff spaces.
In Part 1 of this study we showed, for a wide range of geometries, that the relationships between their concept-sets are fully determined by those between their (affine) automorphism groups. In this (self-contained) part, we show how this…
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…
Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…
In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…
In the present paper, we define a notion of good coverings of Alexandrov spaces with curvature bounded below, and prove that every Alexandrov space admits such a good covering and that it has the same homotopy type as the nerve of the good…
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of…
This paper reviews the equivalence between the category of taut adic spaces that are locally of finite type and the category of strictly analytic Berkovich spaces. An explicit construction of this functor is provided by using the…
We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces.…
We introduce a method that allows to turn topological questions about Hindman spaces into purely combinatorial questions about the Kat\v{e}tov order of ideals on $\mathbb{N}$. We also provide two applications of the method. (1) We…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is…