Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak * denting points norm dense in the unit sphere. A characterisation of Banach spaces whose duals have a corresponding intersection property is established. The question of the density of the strongly exposed po...

Let X be a Hausdorff space and A EX a continuum. A is said to be a Universal Subcontinuum (USC) if AH\B is connected for every continuum B EX. Let a be a collection of USC's of a Hausdorff space. Then a is said to have the finite partition property if a has a decomposition into a finite number of subcollections each having the finite intersection property. A result due to W. J. Gray [l] can be ...

In section 1 we present definitions and basic results concerning the Mazur intersection property (MIP) and some of its related properties as the MIP* . Section 2 is devoted to renorming Banach spaces with MIP and MIP*. Section 3 deals with the connections between MIP, MIP* and differentiability of convex functions. In particular, we will focuss on Asplund and almost Asplund spaces. In Section 4...

for a composition $lambda$ of $n$ our aim is to obtain reduced forms ‎for all the elements in the kazhdan-lusztig (right) cell containing ‎$w_{j(lambda)}$‎, ‎the longest element of the standard parabolic‎ ‎subgroup of $s_n$ corresponding to $lambda$‎. ‎we investigate how far this is possible to achieve by looking at‎ ‎elements of the form $w_{j(lambda)}d$‎, ‎where $d$ is a prefix of ‎an element...

It is proved that a continuum is a tree if and only if each two connected subsets meet in a connected set. In this note a continuum is a compact connected Hausdorff space. A tree is a continuum in which distinct points are never conjugate [6], i.e., any two distinct points are separated by the deletion of some third point. A dendrite is a metrizable tree. The literature is replete with characte...

The purpose of this paper and its sequel is to determine the homotopy groups of the spectrum THH(`). Here p is an odd prime, ` is the Adams summand of p-local connective K-theory (see for example [25]) and THH is the topological Hochschild homology construction introduced by Bökstedt in [3]. In the present paper we will determine the mod p homotopy groups of THH(`) and also the integral homotop...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...