Parametric results for certain infinite-dimensional manifolds (Q1177749)

The theory of \(\mathbb{R}^ \infty\)- and \(Q^ \infty\)-manifolds is generalized in two directions. First, an axiomatic description of different classes of manifolds (so-called \(K^ \infty\)-manifolds) is given. Specializing the space \(K\) to be \(\mathbb{R}^ n\), \(Q^ n\) or \((I^ \tau)^ n\), where \(\tau\) is an uncountable cardinal, the author gets \(\mathbb{R}^ \infty\)-, \(Q^ \infty\)- and \((I^ \tau)^ \infty\)-manifolds. Second, all considerations are in the category \(Top_ B\) (the category of all maps into a given space \(B\)). This allows the author to parametrize the main results of \(\mathbb{R}^ \infty\)- and \(Q^ \infty\)- manifolds. In particular, characterization theorems for trivial and microtrivial \(K^ \infty\)-bundles, theorems for open and closed embeddings and stability theorems are given.