Continuous functions which are defined at almost all points
by
Jorge Martinez
University of Florida
Coauthors: Warren McGovern (Univ. of Houston, Clear Lake)

In a Tychonoff space X, consider the filter F of cofinite dense sets and the ring of quotients C[F] it determines. The article compares C[F] and its bounded subring C^*[F] to a number of ``classical'' rings of quotients of C^*(X). It is determined when C[F] is the maximum ring of quotients of C(X), as long as the cardinality of X is nonmeasurable. The uniform completion of C^*[F] is calculated in terms of the behavior of the oscillation of a function at points outside the maximum domain of the function. It is also shown that C^*[F] is order complete (resp. Dedekind \sigma-complete, resp. Dedekind complete) precisely when X minus a finite set of points is a C^*-space which is also a quasi F-space (resp. basically disconnected, resp. extremally disconnected). Finally, a characterization is given of when C[F] lies in the classical ring of quotients of C(X).

Date received: February 7, 2000