A STUDY ON BAIRE SPACES AND DIMENSION THEORY

Author (s) : MRS. B.PRIYA, M.YAMUNA, MRS.V.NANDHINI

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Abstract :
In this paper we study topological properties of Baire sets in various classes of spaces. The main results state that a Baire set in a realcompact space is realcompact; a Baire set in a topologically complete space is topologically complete; and that a pseudocompact Baire set in any topological space is a zero-set. As a consequence, we obtain new characterizations of realcompact and pseudocompact spaces in terms of Baire sets of their Stone-ech compactifications. (Lorch in [3] using a different method has obtained either implicitly or explicitly the same results concerning Baire sets in realcompact spaces.) The basic tools used for these proofs are first, the notions of anr-compactification andr-embedding (see below for definitions), which have also been defined and used independently byMrwka in [4]; second, the idea included in the proof of the theorem: Every compact Baire set is aG as given inHalmos' text on measure theory [2; Section 51, theorem D].

Keywords : Topology, Topological spces, Discrete Topology

Conference Date : 13/11/2020

Pages : 95

Paper ID : 20095