von Neumann Bornologies and Locally Convex Topologies Determined by Convex Bornologies

For any LCS (X, P https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203749807/1e575708-9d79-4f43-a374-4d458ec8fff6/content/eq2429.tif"/> ), it is known from (13.4)(b) that the von Neumann bornology M von ( P ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203749807/1e575708-9d79-4f43-a374-4d458ec8fff6/content/eq2430.tif"/> and the infracomplete bornology M inf ( P ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203749807/1e575708-9d79-4f43-a374-4d458ec8fff6/content/eq2431.tif"/> are separated, convex bornologies such that M von ( P ) ≤ M inf ( P ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203749807/1e575708-9d79-4f43-a374-4d458ec8fff6/content/eq2432.tif"/>