A weakly Stegall space that is not a Stegall space

A topological space X is said to belong to the class of Stegall (weakly Stegall) spaces if for every Baire (complete metric) space B and minimal usco φ : B2X, φ is single-valued at some point of B. In this paper we show that under some additional set-theoretic assumptions that are equiconsistent with the existence of a measurable cardinal there is a Banach space X whose dual, equipped with the weak topology, is in the class of weakly Stegall spaces but not in the class of Stegall spaces. This paper also contains an example of a compact space K such that K belongs to the class of weakly Stegall spaces but ( C(K), weak) does not

Wijsman Hyperspaces: Subspaces and Embeddings

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.Comment: 6 page

FRAGMENTABILITY BY THE DISCRETE METRIC

Abstract In a recent paper, topological spaces (X, τ) that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are σ-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties. 2010 Mathematics subject classification: primary 46B20; secondary 46B22. Keywords and phrases: fragmentable, sigma-scattered, topological game. In Let (X, τ) be a topological space and let ρ be a metric defined on X. Following [12], we shall say that (X, τ) is fragmented by ρ if whenever ε > 0 and A is a nonempty subset of X there is a τ-open set U such that U ∩ A ∅ and ρ − diam(U ∩ A) < ε. A significant generalisation of fragmentability is the following: a topological space (X, τ), endowed with a metric ρ, is σ-fragmented by ρ if, for each ε > 0, there exists a cover {X ε n : n ∈ N} of X (that is, n∈N X ε n = X) such that for every n ∈ N and every nonempty subset A of X ε n there exists a τ-open set U such that U ∩ A ∅ and ρ − diam(U ∩ A) < ε; see (i) (X, τ) is fragmented by a metric that generates the discrete topology; (ii) (X, τ) is σ-fragmented by the discrete metric; (iii) (X, τ) is σ-scattered, that is, a countable union of scattered spaces. Proof. The proof that (i) ⇒ (ii) follows from [21, Proposition 3.1]. To see that (ii) ⇒ (iii), we simply apply the definition of σ-fragmentability wit

Automatic evaluation of body-related words among young women: an experimental study

Background: Sociocultural models of body image disturbance have linked the development of body dissatisfaction and eating disorders to exposure to media messages depicting the unrealistically slender female physique. Previous research has demonstrated that exposure to images depicting the thin female ideal has negative effects on some females’ levels of body dissatisfaction. Much of this research, however, has utilised relatively long stimulus exposure times; thereby focusing on effortful and conscious processing of body-related stimuli. Relatively little is known about the nature of females’ affective responses to the textual components of body-related stimuli, especially when these stimuli are only briefly encountered. The primary aim of the current research was to determine whether young women automatically evaluate body-related words and whether these responses are associated with body image concerns, including self-reported levels of appearance schematicity, thin internalisation, body dissatisfaction, and dietary restraint. Methods: An affective priming task was used to investigate whether females automatically evaluate body-related words, and whether this is associated with self-reported body image concerns. In a within-participants experimental design, the valence congruence of the prime and target pairs was manipulated. Participants selected body words as primes in Experiment 1 (N = 27), while normatively selected body words were primes in Experiment 2 (N = 50). Each prime was presented briefly, followed by a target word which participants judged as “good” or “bad”. The dependent variable was response latency to the target. Results: Automatic evaluation was evident: responding to congruent pairs was faster than responding to incongruent pairs. Body image concerns were unrelated to automaticity. Conclusions: The findings suggest that brief encounters with body words are likely to prompt automatic evaluation in all young women, and that this process proceeds unintentionally and efficiently, without conscious guidance. The potential implications for higher order, conscious information processing is discussed

Some more recent results concerning weak Asplund spaces

In this paper, we will present some of the latest advances that have occurred in the study of weak Asplund spaces. In particular, we will give an example of a Gâteaux differentiability space that is not weak Asplund

A survey on topological games and their applications in analysis

Abstract. In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.Es este artículo recopilatorio resumimos alguno de los avances recientes en el estudio de los juegos topológicos, así como sus aplicaciones al análisis abstracto. Los temas tratados aquí no representan necesariamente los problemas más importantes del área de los juegos topológicos sino, más bien, una selección de los que interesan a los autores

Null sets and essentially smooth Lipschitz functions

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. Keywords: Lipschitz functions, Haar-null sets, Essentially smooth functions AMS (1991) subject classification: Primary: 49J520; 46N10 Secondary: 58C20. Research supported by NSERC and the Shrum Endowment at Simon Fraser University. y Research supported by a New Zealand Science and Technology Post-Doctoral Fellowship. 2 Jonathan M. Borwein and Warren B. Moors 1 Introduction. The primary purpose of this paper is to introduce a new class of Lipschitz functions and present some of their most fundamental properties. In order to accomplish this goal, we must first extend the notion of a Lebesgue-null set to notion which is valid in any Banach ..