Compactness in asymmetric normed spaces

The Uniform Boundedness Theorem in Asymmetric Normed Spaces

and Applied Analysis 3 The condition of right K-completeness for X, p leaves outside the scope of this theorem an important class of asymmetric normed spaces, the asymmetric normed spaces associated to normed lattices because these spaces are right K-complete only for the trivial case 13 . In this paper, we give a uniform boundedness type theorem in the setting of asymmetric normed spaces which...

D-boundedness and D-compactness in finite dimensional probabilistic normed spaces

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of Dcompactness and D-boundedness in probabilistic normed spaces.

-approximation in normed spaces

ALMOST S^{*}-COMPACTNESS IN L-TOPOLOGICAL SPACES

In this paper, the notion of almost S^{*}-compactness in L-topologicalspaces is introduced following Shi’s definition of S^{*}-compactness. The propertiesof this notion are studied and the relationship between it and otherdefinitions of almost compactness are discussed. Several characterizations ofalmost S^{*}-compactness are also presented.

Compactness in apartness spaces?

In this note, we establish some results which suggest a possible solution to the problem of finding the right constructive notion of compactness in the context of a not–necessarily–uniform apartness space.