In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the ...

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

We introduce the notion centre of a convex set and study space continuous affine functions on compact with centre. show that these spaces are precisely dual base normed in which underlying has (unique) also characterize corresponding norm space. obtain condition compact, balanced, subset locally space, so is an absolute order unit Similarly, we latter becomes absolutely

A widely used theorem of analysis asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of continuous functions. This lemma, variously attributed to Arzela, Escoli, Montel, Vitali, and so on, is of importance in the theory of integral equations, conformal mapping, calculus of variations, and so on. In recent years the lemma has been generalized ...

We call a comb a map f : I → [0,∞), where I is a compact interval, such that {f ≥ ε} is finite for any ε. A comb induces a (pseudo)-distance d̄f on {f = 0} defined by d̄f (s, t) = max(s∧t,s∨t) f . We describe the completion Ī of {f = 0} for this metric, which is a compact ultrametric space called comb metric space. Conversely, we prove that any compact, ultrametric space (U, d) without isolated p...

It was proved by Hurewicz1 that a compact space which is both LC1 and lc" is LCn. In the present paper the corresponding result for locally compact spaces is proved, (a) for uniform local connection, and (b) for relative local connection.2 The extension of Hurewicz's theorem to locally compact spaces is included in (b). The main difficulty in extending Hurewicz's methods is that his "Satz 6," o...

In this paper, we consider the equivariant classification of locally standard 2-torus manifolds. A 2-torus manifold is a closed smooth manifold of dimension n with an effective action of a 2-torus group (Z2) n of rank n, and it is said to be locally standard if it is locally isomorphic to a faithful representation of (Z2) n on R. The orbit space Q of a locally standard 2-torus M by the action i...

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].