FIVE SHORT NOTES ON BOUNDED MAPS
1 Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Oyo, Nigeria
* Corresponding author: sundayoluyemi@njmajournal.com.ng
* Corresponding author: sundayoluyemi@njmajournal.com.ng
Abstract
This paper contributes five observations on bounded maps: (i)
An observation on the definition of a bounded set, (ii) Three
characterizations of bounded linear maps that parallel the usual
general topology characterizations of continuity, (iii) An analogue
of [2, PROPOSITION 3.12.1 p.254][7, Lemma 11.1.1, p.164] for
bounded maps, (iv) That the Banach-Steinhaus Closure Theo
rem is also true for bounded maps, and (v) That the associated
bornological topology is also Hellinger-Teoplitz.
Keywords
Bounded maps
continuity
locally convex spaces.
How to Cite
OLUYEMI, S. (2015). FIVE SHORT NOTES ON BOUNDED MAPS. Nigerian Journal of Mathematics and Applications, 24(1), 87−99.
S. OLUYEMI, "FIVE SHORT NOTES ON BOUNDED MAPS," Nigerian Journal of Mathematics and Applications, vol. 24, no. 1, pp. 87−99, December 2015.
