Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-30T19:39:40.406Z Has data issue: false hasContentIssue false

First-order topological axioms

Published online by Cambridge University Press:  12 March 2014

R. D. Kopperman*
Affiliation:
City University of New York, New York, New York 10031

Abstract

We exhibit a finite list of first-order axioms which may be used to define topological spaces. For most separation axioms we discover a first-order equivalent statement.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ax, J. and Kochen, S., Diophantine problems over local fields. I, American Journal of Mathematics, vol. 87 (1965), pp. 605630.CrossRefGoogle Scholar
[2]Ax, J. and Kochen, S., Diophantine problems over local fields. II, American Journal of Mathematics, vol. 87 (1965), pp. 631648.CrossRefGoogle Scholar
[3]Ax, J. and Kochen, S., Diophantine problems over local fields. III, American Journal of Mathematics, vol. 82 (1966), pp. 432456.Google Scholar
[4]Chang, C. C. and Morel, A., On closure under direct product, this Journal, vol. 23 (1958), pp. 149154.Google Scholar
[5]Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar
[6]Kopperman, R., Model theory and its applications, Allyn & Bacon, Boston, 1972.Google Scholar
[7]Kopperman, R., On the axiomatizability of uniform spaces, this Journal, vol. 32 (1967), pp. 289294.Google Scholar
[8]Kopperman, R., Applications of infinitary languages to analysis, Applications of model theory to algebra, analysis, and probability (Luxemburg, W.A.J., Editor), Holt, Reinhart and Winston, New York, 1969.Google Scholar
[9]Kopperman, R., Continuity spaces (to appear).Google Scholar
[10]Kopperman, R., Length spaces (to appear).Google Scholar
[11]Kowalsky, H. J., Beiträge zur topologischen Algebra, Mathematische Nachrichten, vol. 11 (1954), pp. 143185.CrossRefGoogle Scholar
[12]Nakano, T., On the locally bounded fields, Commentarii Mathematici Universitatis Sancti Pauli, vol. 9 (1961), pp. 7785.Google Scholar