International Conference on Topology and Its Applications
July 3-7, 2023, Nefpaktos, Greece.

http://www.lepantotopology.gr/?section=1880&language=en_US

Title of the talk:
T.M.G.Ahsanullah, Quantale-valued generalizations of approach vector spaces over quantale-valued approach division rings....

Abstract. The motivation of this work is to study the concept of quantalevalued approach vector spaces over the quantale-valued approach division
rings. The reason behind this generalization is crept into the notion of
approach vector spaces attributed to R. Lowen and S. Verwulgen. They
considered approach vector spaces over the reals, whereas our approach is
more general, as we consider arbitrary division rings instead of real vector spaces. In so doing, we first introduce the concepts of approach rings,
approach division rings, and explore some of their basic facts. We determine a suitable class of approach division rings that can be used as a scalar
domain for approach vector spaces, here we talk about the action of approach division ring on approach vector spaces. Furthermore, we generalize
approach rings and approach division rings into quantale-valued approach
rings and quantale-valued approach division rings exploring various results
from quantale-valued approach vector spaces and some of their categorical
aspects.
References
[1] G. J¨ager, Quantale-valued generalizations of approach spaces and quantale-valued topological spaces, Quaest. Math. 42(10)(2019), 1313–1333.
[2] I. Kaplansky, Topological rings, Amer. J. Math. 69(1947), 153–183.
[3] R. Lowen and S. Verwulgen, Approach vector spaces, Houston J. Math.
30(4)(2004), 1127–1142.
[4] L. Nachbin, On the strictly minimal topological division rings, Bull.
Amer. Math. Soc. 55(1949), 1128–1136.