An elementary theory of the category of topological spaces

Author:
Dana I. Schlomiuk

Journal:
Trans. Amer. Math. Soc. **149** (1970), 259-278

MSC:
Primary 18.10

DOI:
https://doi.org/10.1090/S0002-9947-1970-0258914-7

MathSciNet review:
0258914

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Abstract | References | Similar Articles | Additional Information

Abstract: An elementary system of axioms was given by F. W. Lawvere for the category of sets and mappings. The purpose of this paper is to provide a finite number of elementary axioms for the category of topological spaces and continuous mappings and to prove that any model of these axioms is equivalent to ``the category of topological spaces'' constructed over some model of Lawvere's axioms. Furthermore, we prove that any complete category, model of the given axioms is equivalent to the category of topological spaces.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0258914-7

Keywords:
Extremal monomorphism,
regular monomorphism,
regular image,
projective generator,
suitable topology,
exponentiation axiom,
Lawvere's axiom of infinity

Article copyright:
© Copyright 1970
American Mathematical Society