@MISC{Wilson_strictlyirreducible, author = {Terence E. Wilson and Terence E. Wilson}, title = {STRICTLY IRREDUCIBLE MAPS AND STRONG}, year = {} }

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Abstract

Any space X in which no nonvoid open subset is meager is called a Baire space. In this paper, we will consider only T Baire spaces. Given a space X, we will use O(X) 2 to denote the set of all open subsets of X. If F(X) is any family of subsets of X, F+(X) will denote F(X) \ {~}. Thus the expression U E O+(X) indicates that U is a,nonvoid open subset of X. We will denote the collection of meager subsets of X by M(X). For any A C X, M(A) will denote the set of meager points of A, i.e., the set of all x E X such that for some open neighborhood U of x, UnA is meager. M(A) is an open subset of X and A n M(A) is meager in X. * This paper was submitted while I was a graduate student at the University of Delaware. I am grateful to Professor John C. Oxtoby of Bryn Mawr who graciously read the first version of this paper and offered some helpful comments. In particular, I would like to mention that the original version of Lemma 2.2 was incorrect. I also wish to thank the referee for his many helpful comments, correc tions, and considerable patience; he will see his influence. r trust Professor Oxtoby will see the influence of his work. 372 Wilson We will denote X\M(A), the set of nonmeager points of A,