We present a connected version of the compact L-space constructed by Kenneth Kunen under CH. show that this provides Corson space K such Banach C(K) is isomorphic to no continuous function on zero-dimensional compactum.

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

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...

Some cultivars of grapevine have very compact cluster which adversely affect its quality and marketability. ‘Yaghouti’ is a commercial early table grape cultivar that has very compact clusters. The present study was conducted to assess the effects of mechanical and chemical thinning as well as GA3 application on cluster morphology and berry size of grapevine cv. ‘Yaghouti’. Treatments were chem...

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

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...

Let Γ be a group together with a sequence of normal subgroups Γ ⊃ Γ1 ⊃ Γ2 ⊃ . . . of finite index [Γ : Γk] such that T k Γk = {1}. Let (X,Y ) be a (compact) 4n-dimensional Poincaré pair and p : (X,Y )→ (X,Y ) be a Γ-covering, i.e. normal covering with Γ as deck transformation group. We get associated Γ/Γk-coverings (Xk, Yk)→ (X,Y ). We prove that sign(X,Y ) = lim k→∞ sign(Xk, Yk) [Γ : Γk] , whe...

Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.