The convenient category of sequential spaces

Tillotson, Joy Glenys (1978) The convenient category of sequential spaces. Masters thesis, Memorial University of Newfoundland.

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Abstract

It is shown that sequential spaces are a convenient category in the terms of Steenrod’s definition and that they have advantages over other such categories. The method of the Thesis is to define adjoint functors between the categories of all topological spaces and of sequential convergences. Sequential spaces are defined in terms of these functors and results proved for sequential convergences are used in proofs for sequential spaces. Initial and final topologies are used to generalize standard constructions and theorems in these categories. The fibred exponential law and the convergent sequence open topology are discussed in terms of sequential spaces.

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