Topological spaces with a linear basis

Variable-basis topological systems versus variable-basis topological spaces

LoA) and τ is a subalgebra of A . Morphisms (X,A, τ) (f,φ) −−−→ (Y,B, σ) are Set × LoA-morphisms (X,A) (f,φ) −−−→ (Y,B) such that φ ◦ p ◦ f ∈ τ for every p ∈ σ (the so-called continuity). Our definition subsumes the traditional latticevalued approach of [2]. The motivation for the new concept was provided by the problem of doing fuzzy mathematics without order. In [1] the authors consider a rel...

Linear Topological Spaces

On Convex Topological Linear Spaces.

Introduction. In an earlier article [9] the author developed at some length the theory of certain mathematical objects which he called linear systems. It is the purpose of the present paper to apply this theory to the study of convex topological linear spaces. This application is based on the many-to-one correspondence between convex topological linear spaces and linear systems which may be set...

A Note on Linear Topological Spaces*

A space T is called a linear topological space if (1) T forms a linear f space under operations x+y and ax, where x,yeT and a is a real number, (2) T is a Hausdorff topological space,J (3) the fundamental operations x+y and ax are continuous with respect to the Hausdorff topology. The study § of such spaces was begun by A. Kolmogoroff (cf. [4]. Kolmogoroff's definition of a linear topological s...

Boundedness of linear order-homomorphisms in $L$-topological vector spaces

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...