A fixed point index for bimaps
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions onto × ℝcp(X)cp(X). One of these examples is compact. This answers some questions of Arkhangel’skiĭ.
We develop a calculus for the oscillation index of Baire one functions using gauges analogous to the modulus of continuity.
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.