p-Compact, p-Bounded and p-Complete

Authors

  • Rigoberto Vera Mendoza Universidad Michoacana de San Nicolás de Hidalgo

DOI:

https://doi.org/10.4995/agt.2011.1697

Keywords:

Monad, p-compact, p-totally bounded and p-complete space

Abstract

In this paper the nonstandard theory of uniform topological spaces isapplied with two main objectives: (1) to give a nonstandard treatmentof Bernstein’s concept of p-compactness with additional results, (2) tointroduce three new concepts (p,q)-compactness, p-totally boundednessand p-completeness. I prove some facts about them and how these threeconcepts are related with p-compactness.

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Author Biography

Rigoberto Vera Mendoza, Universidad Michoacana de San Nicolás de Hidalgo

Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México.

References

M. Davis, Applied Nonstandard Analysis, John Wiley NY, (1977).

S. Garcia-Ferreira, Comfort types of ultrafilters, Proc. Amer. Math. Soc. 120, no. 4 (1994), 1251–1260.

S. Garcia-Ferreira, Three orderings on (!) !, Topology Appl. 50 (1993), 199–216. http://dx.doi.org/10.1016/0166-8641(93)90021-5

A. Robinson, Non-Standard Analysis, Princeton Landmarks in Math, (1996).

K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Academic Press, (1976).

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How to Cite

[1]
R. Vera Mendoza, “p-Compact, p-Bounded and p-Complete”, Appl. Gen. Topol., vol. 12, no. 1, pp. 17–25, Apr. 2011.

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