Abstract
An analogue of Katětov’s theorem on the equality between the dimension of a Tychonov space and the analytic dimension of its ring of bounded real-valued continuous maps is established for proximity spaces and proximally continuous maps by an internal method of proof. A new kind of filter, called proximally prime filter, arises naturally as a tool in this theory.
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References
Čech, E.: Topological Spaces, Interscience, London, 1966.
Efremovič, V. A.: The geometry of proximity. I., Mat. Sbornik N. S 31(73) (1952), 189 – 200.
Gillman, L. and Jerison, M.: Rings of Continuous Functions, Van Nostrand, Princeton, 1960.
Hejcman, J.: On analytical dimension of rings of bounded uniformly continuous functions, Comment. Math. Univ. Carol 28(1987), 325 – 335.
Herrlich, H.: Topologie II: Uniforme Räume, Heldermann-Verlag, Berlin, 1988.
Isbell, J. R.: Uniform Spaces, American Mathematical Society, Providence, 1964.
Katetov, M.: On rings of continuous functions and the dimension of compact spaces, Casopis Pest Mat. Fys 75 (1950), 1–16 (Russian, English and Czech summaries.)
Naimpally, S. A. and Warrack, B.D.: Proximity Spaces, Cambridge University Press, Cambridge, 1970.
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© 1996 Kluwer Academic Publishers
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Bentley, H.L., Hušek, M., Ori, R.G. (1996). The Katětov Dimension of Proximity Spaces. In: Giuli, E. (eds) Categorical Topology. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0263-3_4
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DOI: https://doi.org/10.1007/978-94-009-0263-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6602-0
Online ISBN: 978-94-009-0263-3
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