This paper is motivated by results of several authors on special types of character spaces, particularly Hausdorff rings, Hausdorff chains and To chains. We develop here a categorical approach based on hom functors and initial structures. This abstract theory accounts for the construction of structure spaces and their salient properties, stressing the role of generalized perfect maps. At the point-set level of the theory some previous studies are simplified here by a different approach.

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Journal General Topology and its Applications
Nel, L. (1976). A categorical approach to topological character theory. General Topology and its Applications, 6(3), 241–258. doi:10.1016/0016-660X(76)90013-1