A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...

We prove a Model Existence Theorem for a fully infinitary logic LA for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson ([7]) and studied in different forms by Anderson ([1]) and Fajardo and Keisler ([2]). This theorem extends Henson’s Compactness Theorem for approximate truth in no...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper we introduce the notion of weak and strong intuitionistic fuzzy (Schauder) basis on an intuitionistic fuzzy n-normed linear space [5] and prove that an intuitionistic fuzzy n-normed linear space having a weak intuitionistic fuzzy basis is separable. Also we discuss approximation property on the same space. Mathematics Subject Classification: 03B20, 03B52, 46A99, 46H25

We start with the definitions of metric spaces and normed spaces. Definition 1 Let X be a set, and let d : X ×X → R ∪ {0}. The pair (X, d) is a metric space if for all x, y, z ∈ X, 1. d(x, y) = d(y, x) 2. d(x, y) = 0 ⇔ x = y 3. d(x, y) + d(y, z) ≥ d(x, z) (triangle inequality) Definition 2 A normed space is R for some finite k together with an associated mapping a → ‖a‖ from R to R ∪ {0} such t...

In this paper, we define 2-normed grand sequence space by inspiration of (Gunawan, 2001) and (Rafeiro et. al., 2018). Also, give some basic properties these spaces.

Using the notion of a Banach operator, we have obtained a decompositional property of a Hilbert space, and the equality of two invertible bounded linear multiplicative operators on a normed algebra with identity. 1. Introduction. This paper is a continuation of our earlier work [7] on Banach operators. We recall that if X is a normed space and α : X → X is a mapping, then following [4], α is sa...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

As application of complete metric space, we proved a Baire’s category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space ge...