Related papers: Round and sleek topological spaces

What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…

We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…

We investigate several boundedness properties of function spaces considered as uniform spaces.

We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.

In this paper, we work on the structure of soft linear spaces over a field K and investigate some of its properties. Here, we use the concept of the soft point which was introduced in [2,6]. We then introduce the soft norm in soft linear…

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

We examine some kinds of discrete symmetries which are dynamically preserved, using the (generalized) Gowdy models of the first kind.

The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…

We give a simple description of the topology of free topological vector space $\mathbb{V}(X)$ and the topology of the free locally convex space $L(X)$ over a Tychonoff space $X$. The case when $X$ is a pseudocompact space is also…

Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…

We study conditions under which a space that has a good property and a courser topology with another good property admits a continuous bijection onto a space with both properties.

In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.

We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space…

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.