Spaces with σ-point finite bases

Spaces with Σ-locally Countable Weak-bases

In this paper, spaces with σ-locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or g-first countable spaces with σ-locally countable cs-networks). To find the internal characterizations of certain images of metric spaces is an interesting research topic on general topology. Recently, S. Xia introduced the concept of weakly open mappings, by using it,...

σ-Normality of Topological Spaces

Wave Equations with Point Interactions in Finite Energy Spaces

Given the abstract wave equation φ̈−∆αφ = 0, where ∆α is the Laplace operator with a point interaction of strength α, we define and study W̄α, the associated wave generator in the phase space of finite energy states. We prove the existence of the phase flow generated by W̄α, and describe its most relevant properties with particular emphasis on the associated symplectic structure and scattering the...

LOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES

In this paper, the concept of {sl local base with  stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.

Unconditional Bases and Unconditional Finite-dimensional Decompositions in Banach Spaces

Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...