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On chirality groups and regular coverings of regular oriented hypermaps

Antonio Breda d'Azevedo, Ilda Inácio Rodrigues, Maria Elisa Fernandes (2011)

Czechoslovak Mathematical Journal

We prove that if the Walsh bipartite map = 𝒲 ( ) of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps ( 3 , 3 , 3 ) b , c = 𝒲 - 1 { 6 , 3 } b , c induced by the family of toroidal bipartite maps...

On closed sets with convex projections in Hilbert space

Stoyu Barov, Jan J. Dijkstra (2007)

Fundamenta Mathematicae

Let k be a fixed natural number. We show that if C is a closed and nonconvex set in Hilbert space such that the closures of the projections onto all k-hyperplanes (planes with codimension k) are convex and proper, then C must contain a closed copy of Hilbert space. In order to prove this result we introduce for convex closed sets B the set k ( B ) consisting of all points of B that are extremal with respect to projections onto k-hyperplanes. We prove that k ( B ) is precisely the intersection of all k-imitations...

On closed subgroups of the group of homeomorphisms of a manifold

Frédéric Le Roux (2014)

Journal de l’École polytechnique — Mathématiques

Let M be a triangulable compact manifold. We prove that, among closed subgroups of Homeo 0 ( M ) (the identity component of the group of homeomorphisms of M ), the subgroup consisting of volume preserving elements is maximal.

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