Topological and Limit-Space Subcategories of Countably-Based Equilogical Spaces

@article{Menni2002TopologicalAL,
title={Topological and Limit-Space Subcategories of Countably-Based Equilogical Spaces},
author={Mat{\'i}as Menni and Alex K. Simpson},
journal={Mathematical Structures in Computer Science},
year={2002},
volume={12},
pages={739-770}
}

There are two main approaches to obtaining “topological” cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed — for example, the category of sequential spaces. Under the other, one generalises the notion of space — for example, to Scott’s notion of equilogical space. In this paper we show that the two approaches are equivalent for a large class of objects. We first observe that the category of countably… CONTINUE READING