JARAK FUNGSI KE RUANG FUNGSI BAIRE KELAS SATU; THE DISTANCE OF A FUNCTION TO SPACES OF BAIRE ONE FUNCTIONS

I MADE ARI SUSENA, Atok Zulijanto

2013 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

The distance of a point x to a set A in a metric space is defined by the supremum of the distances of x to each point in the set A. In this thesis, we will discuss about the distance of a function f : X ! E to B1(X;E), where B1(X;E) denotes the space of Baire one functions from a metric space X to a Banach space E. In order to find the distance estimation, we will use two concepts, that are concept of index fragmentability and concept of oscillation function. As a consequence of the estimation result by using oscillation concept is for every separately continuous function f : X ? K ! R where X is a completely metrizable topological space and K is a compact topological space, there is a G?-dense set D ? X such that f continuous on D ? K

Kata Kunci : JARAK FUNGSI; RUANG FUNGSI; BAIRE KELAS SATU