When a totally bounded group topology is the Bohr topology of a LCA group
نویسندگان
چکیده
منابع مشابه
Discrete sets and the maximal totally bounded group topology*
Hart, K.P. and J. van Mill, Discrete sets and the maximal totally bounded group topology, Journal of Pure and Applied Algebra 70 (1991) 73-80. If G is an Abelian group, then G # is G with its maximal totally bounded group topology. We prove that every A c G# contains a closed (in G#) and discrete subset B such that lB1 = IAl. This answers a question posed by Eric van Douwen. We also present an ...
متن کامل2 the Bohr Topology
We prove a Ramsey-style theorem for sequences of vectors in an innnite-dimensional vector space over a nite eld. As an application of this theorem, we prove that there are countably innnite Abelian groups whose Bohr topologies are not homeomorphic.
متن کاملThe topology of a semisimple Lie group is essentially unique
We study locally compact group topologies on simple and semisimple Lie groups. We show that the Lie group topology on such a group S is very rigid: every “abstract” isomorphism between S and a locally compact and σ -compact group Γ is automatically a homeomorphism, provided that S is absolutely simple. If S is complex, then noncontinuous field automorphisms of the complex numbers have to be con...
متن کاملSome Facets of an Lca Group inside Its Bohr Compactification
Let be a non-discrete LCA (locally compact abelian) group, its dual. ( ) ∧, where denotes discrete, is the Bohr compactification of , denoted by . There exists a continuous group isomorphism ί: → of onto a proper dense subgroup of . This subgroup to be denoted by ί is the main object of our study. A subgroup of is pure if ∩ = for each positive integer . We define to be strongly pure if is pure ...
متن کاملGroup Splittings and Asymptotic Topology
It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspheri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2019
ISSN: 0166-8641
DOI: 10.1016/j.topol.2019.02.025