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We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some…
In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem which states that every $T_1$ asymmetric normed space with…
The idea of convex sets and various related results in 2-Probabilistic normed spaces were established in [HR]. In this paper, We obtain the concepts of convex series closedness, convex series compactness, boundedness and their…
In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.
In a countably normed space which is a linear space equipped with a countable number of pair-wise compatible norms, we prove the existence of a common nearest point (in all norms) from a point outside a nonempty subset if this subset is…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
The paper studies a general norm minimization problem on a product of normed vector spaces. We establish dual necessary and sufficient optimality conditions and derive explicit formulas for the corresponding solution sets. These formulas…
In this paper, we show that D-compactness in Generalized \v{S}erstnev spaces implies D-boundedness and as in the classical case, a D-bounded and closed subset of a characteristic Generalized \v{S}erstnev is not D-compact in general.…
We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log (dim X) = O(log (dim V)) and (2) every…
The motivation of this paper is a suggestion by H\"ole of comparing the notions of $\D$-boundedness and boundedness in Probabilistic Normed spaces (briefly PN spaces), with non necessarily continuous triangle functions. Such spaces are here…
Relying on Kolmogorov's classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normable…
We consider the equivalence of some norms in Sobolev spaces on bounded domains of the d-dimensional real Euclidean space and also in Sobolev spaces on the boundaries of those domains.
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.
It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentially weakly lower semicontinuous coercive functions on…
A Banach space (or its norm) is said to have the diameter $2$ property (D$2$P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter $2$. We construct an equivalent norm on $L_1[0,1]$ which is weakly…
In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\cite{Sa}, \cite{CaSoA}). However, the question for multidimensional Lorentz spaces is still open. In this paper,…
This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm…
An equilateral dimension of a normed space is a maximal number of pairwise equidistant points of this space. The aim of this paper is to study the equilateral dimension of certain classes of finite dimensional normed spaces. The well-known…
We study completeness of the spaces $\mathcal{P}_s^=$ of probability measures in $\mathbb{R}^N$ which have equal (prescribed) moments up to order $s \in \mathbb{N}$, endowed with the metric $d_s(\mu,\nu)=\sup_{x \in \mathbb{R}^N\setminus…
We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is $1$. As a tool to obtain the main result we establish…