Abstract
This chapter discusses various methods of introducing topologies onto a collection of mappings and of approximating a continuous function over a T2-space by special functions. It discusses the extent the properties of the range space and domain space of a continuous mapping will affect each other. Every metric space is the image of a zero-dimensional metric space by a compact, closed, and continuous mapping. The chapter discusses countably compact closed mappings onto metric spaces. A topological space R is called an M-space if there is a metric space S and a countably compact, closed, and continuous mapping of R onto S. Such a mapping is called a quasi-perfect mapping. Therefore, every metrizable space and every countably compact space is an M-space. The chapter also describes relations among various generalized metric spaces.
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