Warren B. Moors

Topological games and topological groups

The thermostability of shaped articles of thermoplastic material is determined by the visible alteration of the surface of the article caused by a focused hot gas jet which is blown onto the surface. The temperature of the gas and the gas rate hitting the surface per unit of time, and also the residence time of the shaped article under the influence of the hot gas jet are a measure for the thermostability.

Continuity points of quasi-continuous mappings

Abstract It is known that the fragmentability of a topological space X by a metric whose topology contains the topology of X is equivalent to the existence of a winning strategy for one of the players in a special two players “fragmenting game”. In this paper we show that the absence of a winning strategy for the other player is equivalent to each of the following two properties of the space X : for every quasi-continuous mapping f :Z→X , where Z is a complete metric space, there exists a point z 0 ∈Z at which f is continuous; for every quasi-continuous mapping f :Z→X , where Z is an α -favorable space, there exists a dense subset of Z at the points of which f is continuous. In fact, we show that the set of points of continuity of f is of the second Baire category in every non-empty open subset of Z . Using this we derive some results concerning joint continuity of separately continuous functions.

Generic continuity of minimal set-valued mappings

We study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gs subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and a-fragmentability of the weak topology. A characterisation of non membership is used to show that lx(t>l) is not a member of our classes of generic continuity spaces. 1991 Mathematics subject classification (Amer. Math. Soc): primary 46B22; secondary 46B20, 58C20.

Separable determination of integrability and minimality of the Clarke subdifferential mapping

In this paper we show that the study of integrability and

Null Sets and Essentially Smooth Lipschitz Functions

D

Lipschitz functions with prescribed derivatives and subderivatives

-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.

A Gâteaux differentiability space that is not weak Asplund

In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.

A weak Asplund space whose dual is not weak* fragmentable

In general it is difficult to construct Lipschitz functions which are not directly built up from either convex or distance functions. One impediment to such constructions is that outside of the real line it is difficult to find anti-derivatives. The main result of this paper provides, under suitable circumstances, a technique for constructing such anti-derivatives. More precisely, we show that if

A characterisation of minimal subdifferential mappings of locally Lipschitz functions

f_{1}

Generic continuity of restricted weak upper semi-continuous set-valued mappings

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