On homeomorphism groups of non-compact surfaces, endowed with the Whitney topology

Банах, Тарас; Mine, Kotaro; Sakai, Katsuro; Yagasaki, Tatsuhiko

doi:10.1016/j.topol.2013.12.013

Cited by 3 publications

(2 citation statements)

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“…Combining this fact with Theorems 1.4, 1.5 and Proposition 4.2, we obtain the following criterion, which is the main result of this paper. This criterion has been applied in [1] and [6] for recognizing the topology of some homeomorphism and diffeomorphism groups. Theorem 1.6.…”

Section: Introductionmentioning

confidence: 99%

Detecting topological groups which are (locally) homeomorphic to LF-spaces

Банах

Mine

Repovš

et al. 2013

Topology and its Applications

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We prove that a topological group G is (locally) homeomorphic to an LF-space if G = n∈ω Gn for some increasing sequence of subgroups (Gn)n∈ω such that (1) for any neighborhoods Un ⊂ Gn, n ∈ ω, of the neutral element e ∈ Gn ⊂ G, the set(2) each group Gn is (locally) homeomorphic to a Hilbert space;(3) for every n ∈ N the quotient map Gn → Gn/G n−1 is a locally trivial bundle; (4) for infinitely many numbers n ∈ N each Z-point in the quotient space Gn/G n−1 = {xG n−1 : x ∈ Gn} is a strong Z-point.2010 Mathematics Subject Classification. 57N20; 46A13; 22A05.

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Section: Introductionmentioning

confidence: 99%

Detecting topological groups which are (locally) homeomorphic to LF-spaces

Банах

Mine

Repovš

et al. 2013

Topology and its Applications

View full text Add to dashboard Cite

show abstract

“…In this paper we shall present a simple criterion for recognizing topological spaces that are homeomorphic to (open subspaces of) LF -spaces. This criterion has been applied in [3], [4] and [7] for detecting topological groups that are homeomorphic to (open subspaces of) LF-spaces.…”

Section: Introductionmentioning

confidence: 99%