Bornological versus topological analysis in metrizable spaces

Details Bornological versus topological analysis in metrizable spaces Bornological versus topological analysis in metrizable spaces

2003-10-15

arxiv.org/abs/math/0310225v2

Mathematics

Functional Analysis

I only corrected a few typos

Scientific paper

Given a metrizable topological vector space, we can also use its von Neumann bornology or its bornology of precompact subsets to do analysis. We show that the bornological and topological approaches are equivalent for many problems. For instance, they yield the same concepts of convergence for sequences of points or linear operators, of continuity of functions, of completeness and completion. We also show that the bornological and topological versions of Grothendieck's approximation property are equivalent for Frechet spaces. These results are important for applications in noncommutative geometry. Finally, we investigate the class of ``smooth'' subalgebras appropriate for local cyclic homology and apply some of our results in this context.

Affiliated with

Also associated with

No associations

Rating

Bornological versus topological analysis in metrizable spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bornological versus topological analysis in metrizable spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bornological versus topological analysis in metrizable spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-527720