Affiliation:
1. Department of Pure Mathematics, University of Calcutta, Kolkata, India
2. Department of Commerce (E), St. Xavier’s college, Kolkata, India
Abstract
In this article, we continue our study of the ring of Baire one functions on
a topological space (X,?), denoted by B1(X), and extend the well known M.
H. Stones?s theorem from C(X) to B1(X). Introducing the structure space of
B1(X), an analogue of Gelfand-Kolmogoroff theorem is established. It is
observed that (X,?) may not be embedded inside the structure space of
B1(X). This observation inspired us to introduce a weaker form of embedding
and show that in case X is a T4 space, X is weakly embedded as a dense
subspace, in the structure space of B1(X). It is further established that
the ring B*1(X) of all bounded Baire one functions, under suitable
conditions, is a C-type ring and also, the structure space of B*1(X) is
homeomorphic to the structure space of B1(X). Introducing a finer topology ?
than the original T4 topology ? on X, it is proved that B1(X) contains free
maximal ideals if ? is strictly finer than ?. Moreover, in the class of all
perfectly normal T1 spaces, ? = ? is necessary as well as sufficient for B1(X)
= C(X).
Publisher
National Library of Serbia
Cited by
1 articles.
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