p-Compact, p-Bounded and p-Complete
Submitted: 2013-09-16
|Accepted:
|Funding Data
Downloads
Keywords:
Monad, p-compact, p-totally bounded and p-complete space
Supporting agencies:
This research was not funded
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.
Show more
Show less
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).
