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This study first provides a brief overview of the structure of typicalGrassmann manifolds. Then a new type of supergrassmannians is construced usingan odd involution in a super ringed space and by gluing superdomains together.Next, constructing a Gauss morphism of a super vector bundle, some propertiesof this morphism is discussed. By this, we generalize one of the main theoremsof homotopy classification for vector bundles in supergeometry. Afterwards, asimilar structure is introduced in the state of infinite-dimensional. Here ourtools mainly include multilinear algebra of Grassmann algebras, the directlimit of the base spaces and the inverse limit of the structure sheaf of ringedspaces. We show that the resulting super vector bundle is a universal member ofits category.

Homotopy Classification of Super Vector Bundles and Universality