Related papers: Extremally $T_1$-spaces and Related Spaces
In a series of three papers we develop an end space theory for digraphs. Here in the second paper we introduce the topological space $|D|$ formed by a digraph $D$ together with its ends and limit edges. We then characterise those digraphs…
We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…
Let c=2^aleph0 denote the cardinality of the continuum and let a,b,k be infinite cardinal numbers with a<b\leq 2^a. We show that there exist precisely 2^b T0-spaces of size a and weight b up to homeomorphism. Among these non-homeomorphic…
We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…
This article introduces strongly near proximity, which represents a new kind of proximity called \emph{almost proximity}. A main result in this paper is the introduction of a hit-and-miss topology on ${CL}(X)$, the hyperspace of nonempty…
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special,…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
We consider a new class of open covers and classes of spaces defined from them, called "iota spaces". We explore their relationship with epsilon-spaces (that is, spaces having all finite powers Lindelof) and countable network weight. An…
We discuss supernear spaces.
We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex $X$ including their connectivity and their top homology groups. It also discusses the inclusion of the…
The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…
For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on X with the compact-open topology. In this paper, we have gave characterization for $C_k(X)$ to satisfy $S_{fin}(S, S)$.
The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
A horoboundary is one of the attempts to compactify metric spaces, and is constructed using continuous functions on metric spaces. It is a concept that includes global information of metric spaces, and its correspondence with an ideal…
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form $T[(M_k,\theta_k)_{k=1}^{\ell}]$ with index $i(M_k)$ finite are either $c_0$ or $\ell_p$ saturated for some $p$ and we…