Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University468610.18287/2541-7525-2013-19-9.1-49-57TOPOLOGICAL FREEDOM FOR CLASSICAL AND QUANTUM NORMED MODULESShteinerS.M.morenov.sv@ssau.ruLomonosov Moscow State University01092013199.149570506201705062017Copyright © 2013, Shteiner S.2013In the article questions, connected with the notion of topological projectiv-ity are viewed. It is shown that this type of projectivity can be represented as a partial case of certain general-categorical scheme, based on a notion of framed category. Apart from that topologically free 'classical', as well as quantum normed modules are described. Analogous results were obtained for topo-logical injectivity.topological freedom, topological cofreedom, semilinear normed space, quantum normed spaceтопологическая свобода, топологическая косвобода, полу- линейное нормированное пространство, квантовое нормированное пространство