On Point Wise Products of Uniformly
Continuous Functions on Uniform Space

Ku. S.B.Tadam; Dr. S.M.Padhye

doi:https://doi.org/10.14445/22315373/IJMTT-V43P528

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 3 | Year 2017 | Article Id. IJMTT-V43P528 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P528

On Point Wise Products of Uniformly Continuous Functions on Uniform Space

Ku. S.B.Tadam, Dr. S.M.Padhye

Citation :

Ku. S.B.Tadam, Dr. S.M.Padhye, "On Point Wise Products of Uniformly Continuous Functions on Uniform Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 3, pp. 234-237, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P528

Abstract

In this paper we obtain the sufficient conditions on a uniform space (x,u) for which uc(x), the family of all uniformly continuous functions on x is an algebra. It is proved that Theorem A: If (x,u) is a uniformly continuous uniform space then uc(x), is an algebra. Theorem B:If is precompact uniform space. Then is an algebra. We prove that ucR(x), the family of all uniformly continuous real valued functions on x is a lattice of functions which need not be a complete lattice in the sense that every subset of ucR(x) may not have supremum or infimum in ucR(x) by providing a counter example.

Keywords

Uniform space, Uniformly continuous space, Lattice, Complete Lattice.

References

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