The topological structure of a certain Menger space (Q2371838)

The article is devoted to probabilistic normed spaces, which include in particular Menger and Serstnev spaces. Their local convexity in a strong topology is studied. Then bounded linear operators on probabilistic normed spaces are investigated. A characterization of bounded operators between two probabilistic normed spaces in terms of families of probabilistic norms of operators is given. It is proved that a space of strongly bounded linear operators between two probabilistic normed spaces can be endowed with a probabilistic norm.