p-Compact, p-Bounded and p-Complete

Rigoberto Vera Mendoza
DOI: https://doi.org/10.4995/agt.2011.1697

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.

Keywords

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

Full Text:

PDF

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).

Abstract Views

4866
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share


Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt