It is known that a real valued measure (1) on the a-ring of Baire sets of a locally compact Hausdorff space, or (2) on the Borel sets of a complete separable metric space is regular. Recently Dinculeanu and Kluvanek used regularity of non-negative Baire measures to prove that any Baire measure with values in a locally convex Hausdorff topological vector space (TVS) is regular. Subsequently a di...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...

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.

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

In the Hyperbolic space Hn (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in Hn globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n− 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n−1)-flats of the resulting hypersu...

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.