in this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.

This document is a summary of basic facts about the “standard” category of compactly generated spaces introduced by McCord [McC69] (often referred to in the literature as “compactly generated weak Hausdorff spaces”, or “weak Hausdorff k-spaces”). The main references I’ve used for this material are Gaunce Lewis’s thesis [Lew, App. A], and Neil Strickland’s note [Str09] (especially for material a...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

For any countable CW -complex K and a cardinal number τ ≥ ω we construct a completely metrizable space X(K, τ) of weight τ with the following properties: e-dimX(K, τ) ≤ K, X(K, τ) is an absolute extensor for all normal spaces Y with e-dimY ≤ K, and for any completely metrizable space Z of weight ≤ τ and e-dimZ ≤ K the set of closed embeddings Z → X(K, τ) is dense in the space C(Z,X(K, τ)) of al...

The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of C for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely, E k(f,X) (−→ 1/k, f,X ) , where E k(f,X) is the deviation of the best approximation of f ∈ X by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and ...

For every space X let K(X) be the set of all compact subsets of X . Christensen [6] proved that if X, Y are separable metrizable spaces and F : K(X) → K(Y ) is a monotone map such that any L ∈ K(Y ) is covered by F (K) for some K ∈ K(X), then Y is complete provided X is complete. It is well known [3] that this result is not true for non-separable spaces. In this paper we discuss some additional...