FUNGSI BAIRE-1 PADA RUANG TOPOLOGI - , HERI SETIAWAN ([Yogyakarta] : Universitas Gadjah Mada, 2013)
In this final project we discuss about Baire-1 functions on topological spaces. A real-valued function f on a topological space is called Baire-1 function if it is a pointwise limit of a sequence of continuous functions. A Baire-1 function on a perfectly normal space can be characterized by open sets and F sets, that is a function f : X ! R where X is a perfectly normal space, is Baire-1 if and only if for any open set U R, the preimage fô1(U) is an F set. Some properties of Baire-1 functions that we discuss in this final project are the uniform limit of any sequence of Baire-1 functions is a Baire-1 function and the set of all continuity points of a Baire-1 function on a Baire space is a dense set. In this final project we also discuss about B1-retract sets. A B1-retract set is the extension of a retract set. A B1-retract set is obtained by replacing the continuous function in the definition of retract set with a Baire-1 function.