today each city due to natural limitations, facilities and planning policies has different growth pattern which according to its spread, has different consequences and results. although there is a wide range of urban growth patterns, but the important thing is not diversity and number of models but is the absence of rules and methods of transition from one to another pattern (form). so this art...

This note is a survey of J-spaces. A space X is a J-space if, whenever {A, B} is a closed cover of X with A ∩ B compact, then A or B is compact. A space X is a strong J-space if every compact K ⊂ X is contained in a compact L ⊂ X with X\L connected. [As in [4], all maps are continuous and all spaces are Hausdorff.] 1.1. Every strong J-space X is a J-space. The two concepts coincide when X is lo...

We investigate the problem of existence a bounded extension to $C(K)$ $c_0(I)$-valued operator $T$ defined on subalgebra induced by continuous increasing surjection $\phi :K\to L$, where $K$ and $L$ are compact lines. Gener

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact $L^{p_1}(w_1)$ $w_1\in R^d)$. Then $L^p(w)$ $p\in(1,\infty)$ $w\in A_p(\mathbb This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from combination results the interpolation theory spaces one h...

We prove that a Banach space E has the compact range property (CRP) if and only if for any given C∗-algebra A, every absolutely summing operator from A into E is compact. Related results for p-summing operators (0 < p < 1) are also discussed as well as operators on non-commutative L-spaces and C∗-summing operators.

This paper deals with the compact trace theorem in domains Ω ⊂ R 3 with external cusps. We show that if the power sharpness of the cusp is bellow a critical exponent, then the trace operator γ : H(Ω) → L(∂Ω) exists and it is compact.

This paper shows necessary and sufficient conditions on subsets of variable exponent spaces Lp(?)(?) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. As application, we prove that all separable Banach-Saks. Also, L-weakly compact inclusions between studied.

Extending work of [14, 16, 26], we show there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable L-spaces or compact S-spaces. The model is one of the form PFA(S)[S], where S is a coherent Souslin tree.

An absolute ideal of an Abelian group G is a subgroup that in every ring whose additive coincides with G. We describe reduced algebraically compact groups admit at least one structure R such (Problem 93 L. Fuchs’ book “Infinite Groups”). Reduced, compact, have only fully invariant subgroups as are characterized.