Parametric results for certain infinite-dimensional manifolds
The theory of R∞-(Q∞-) manifolds is generalized in two directions. Firstly, an axiomatical approach is proposed to describing various classes of manifolds (so-called K∞-manifolds) including, along with the indicated classes of R∞and Q∞-manifolds, also, e.g., the manifolds modeled on the space, where τ is a cardinal. Secondly, all the arguments were carried out in the category TopB, which makes it possible to carry over from spaces to maps practically all basic results of the theory of R∞-(Q∞-) manifolds. Specifically, there are obtained characterization theorems for trivial and microtrivial K∞-fibrations, theorems on open and closed embeddings, stability thoerems, etc.
KeywordsBasic Result Axiomatical Approach Characterization Theorem Closed Embedding
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