IJPAM: Volume 120, No. 4 (2018)

Title

BOUNDEDNESS ON UNIFORM SPACES AND IT'S MAPPINGS

Authors

M. Moosaei$^1$, Gh.R. Rezaei$^2$, J. Jamalzadeh$^3$
$^{1,2,3}$Department of mathematics
University of Sistan and Baluchestan
Zahedan, IRAN

Abstract

In this note we introduce a boundedness on uniform spaces. We study some properties of corresponding bounded sets. So we introduce two types of mappings on uniform spaces from the perspective of the given boundedness. We compare them to each other and with the class of uniformly continuous mappings. Finally we equip these classes of mappings with the topology of uniform convergence induced by the uniformity of uniform convergence. We show some of these classes of mappings form complete uniform spaces provided the range space is complete.

History

Received: January 26, 2017
Revised: February 15, 2019
Published: February 17, 2019

AMS Classification, Key Words

AMS Subject Classification: 54E15, 34C11, 54C35, 42A65
Key Words and Phrases: uniform space; bounded set; bounded mapping; uniformly continuous mapping; completeness

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How to Cite?

DOI: 10.12732/ijpam.v120i4.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 4
Pages: 563 - 572


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