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A unified approach, that uses countable sets with convergences and basics of the theory of LF -spaces, is given to some old results of the Silverman–Toeplitz type obtained in the late 1930's by H.J. Hamilton for matrix transformations of multiple sequences. [ABSTRACT FROM AUTHOR]

Suppose M is a non-compact connected n -manifold without boundary, D ( M ) is the group of C ∞ -diffeomorphisms of M endowed with the Whitney C ∞ -topology and D 0 ( M ) is the identity connected component of D ( M ) , which is an open subgroup in the group D c ( M ) ⊂ D ( M ) of compactly supported diffeomorphisms of M . It is shown that D 0 ( M ) is homeomorphic to N × R ∞ for an l 2 -manifold N whose topological type is uniquely determined by the homotopy type of D 0 ( M ) . For instance, D 0 ( M ) is homeomorphic to l 2 × R ∞ if n = 1 , 2 or n = 3 and M is orientable and irreducible. We also show that for any compact connected n -manifold N with non-empty boundary ∂ N the group D 0 ( N ∖ ∂ N ) is homeomorphic to D 0 ( N ; ∂ N ) × R ∞ , where D 0 ( N ; ∂ N ) is the identity component of the group D ( N ; ∂ N ) of diffeomorphisms of N that do not move points of the boundary ∂ N . [ABSTRACT FROM AUTHOR]

Abstract: We prove that for any non-compact connected surface M the group of compactly supported homeomorphisms of M endowed with the Whitney topology is homeomorphic to or . [Copyright &y& Elsevier]

Abstract: We prove that a topological group G is (locally) homeomorphic to an LF-space if for some increasing sequence of subgroups such that [(1)] for any neighborhoods , , of the neutral element , the set is a neighborhood of e in G; [(2)] each group is (locally) homeomorphic to a Hilbert space; [(3)] for every the quotient map is a locally trivial bundle; [(4)] for infinitely many numbers each Z-point in the quotient space is a strong Z-point. [Copyright &y& Elsevier]

Abstract: We present a topological characterization of LF-spaces and detect small box-products that are (locally) homeomorphic to LF-spaces. [Copyright &y& Elsevier]

Abstract: Let X be a locally compact Polish space and G a non-discrete Polish ANR group. By , we denote the topological group of all continuous maps endowed with the Whitney (graph) topology and by the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete then the space is an -manifold. In this article we show that if X is non-compact and not end-discrete then is an -manifold, and moreover the pair is locally homeomorphic to the pair of the box and the small box powers of . [Copyright &y& Elsevier]

Let ( M′, F′) and ( M, F) be two (compact or not) foliated manifolds, C∞ F( M′, M) the space of smooth maps which send leaves into leaves. In this paper we prove that C∞ F( M′, M) admits a structure of an infinite-dimensional manifold modeled on LF-spaces, provided that F is a Riemannian foliation or, more generally, when it admits an adapted local addition. [ABSTRACT FROM AUTHOR]