Stationary and convergent strategies in Choquet games

If NONEMPTY has a winning strategy against EMPTY in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows NONEMPTY to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits NONEMPTY to consider the previous move by EMPTY. We show that NONEMPTY has a stationary winning strategy for every second countable T1 Choquet space. More generally, NONEMPTY has a stationary winning strategy for any T1 Choquet space with an open-finite basis. We also study convergent strategies for the Choquet game, proving the following results. (1) A T1 space X is the open image of a complete metric space if and only if NONEMPTY has a convergent winning strategy in the Choquet game on X. (2) A T1 space X is the compact open image of a metric space if and only if X is metacompact and NONEMPTY has a stationary convergent strategy in the Choquet game on X. (3) A T1 space X is the compact open image of a complete metric space if and only if X is metacompact and NONEMPTY has a stationary convergent winning strategy in the Choquet game on X.Comment: 24 page

Reverse Mathematics and Algebraic Field Extensions

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $\mathsf{WKL}_0$ is equivalent to the ability to extend $F$-automorphisms of field extensions to automorphisms of $\bar{F}$, the algebraic closure of $F$. Section 3 explores finitary conditions for embeddability. Normal and Galois extensions are discussed in section 4, and the Galois correspondence theorems for infinite field extensions are treated in section 5.Comment: 25 page

Les crises actuelles de l’homme : les comprendre, s’en déprendre

Quatre crises interpellent l'homme moderne : crise de l'identité, crise du désir, crise relationnelle et crise de la parentalité. L'auteur explique en quoi consiste chacune d'elles et dégage quelques perspectives d'intervention individuelle et collective susceptibles d'aider à leur résolution

La persistance aux études, défi premier en formation à distance /

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La perception de l’agression sexuelle chez des garçons qui en ont été victimes durant l’enfance ou l’adolescence

Le présent article fait état d'une étude qualitative menée auprès de trente jeunes hommes québécois âgés de 16 à 44 ans qui ont été sexuellement agressés par des hommes au cours de leur enfance ou de leur adolescence. Une expérience traumatisante comme l'abus sexuel, surtout si elle est vécue en bas âge, n'a pas de sens a priori. Dans sa construction de soi et du monde, le garçon abusé tentera donc de lui trouver une signification, une rationalité quelconque, sinon une raison d'être. Tel est l'aspect particulier et peu traité sur lequel se penche cet article. Extrait d'un rapport de recherche à paraître, il aborde la perception subjective de l'abus sexuel chez les garçons qui en furent victimes.This article presents some results of a qualitative study carried out among 30 young men aged between 16 and 44 who have been sexually abused by men during their childhood or adolescence. Such a traumatizing experience does not seem to make any sense. In constructing himself and the world around him, the abused boy will try to find some explanation for it, some reason for being. The article deals with this particular and rarely discussed aspect of the abuse. Taken from a research report to be published, it deals with the way young men perceive the sexual abuse they suffered