Countable products and sums of lines and circles: their closed subgroups, quotients and duality properties
R Brown, PJ Higgins, SA Morris - Mathematical Proceedings of the …, 1975 - cambridge.org
R Brown, PJ Higgins, SA Morris
Mathematical Proceedings of the Cambridge Philosophical Society, 1975•cambridge.orgIt is well-known ((2), Theorem 9· 11) that any closed subgroup of Rn is isomorphic
(topologically and algebraically) to Ra× Zb, where a, b are suitable non-negative integers.
For an infinite product of copies of R, it is also known that any locally compact (hence
closed) subgroup is a product of copies R and Z, and that any connected subgroup is a
product of copies of R (see (7),(3), respectively). Some information is also given in (3) on
closed subgroups of products of copies of R and T, where T= R/Z is the circle group.
(topologically and algebraically) to Ra× Zb, where a, b are suitable non-negative integers.
For an infinite product of copies of R, it is also known that any locally compact (hence
closed) subgroup is a product of copies R and Z, and that any connected subgroup is a
product of copies of R (see (7),(3), respectively). Some information is also given in (3) on
closed subgroups of products of copies of R and T, where T= R/Z is the circle group.
It is well-known ((2), Theorem 9·11) that any closed subgroup of Rn is isomorphic (topologically and algebraically) to Ra × Zb, where a, b are suitable non-negative integers. For an infinite product of copies of R, it is also known that any locally compact (hence closed) subgroup is a product of copies R and Z, and that any connected subgroup is a product of copies of R (see (7), (3), respectively). Some information is also given in (3) on closed subgroups of products of copies of R and T, where T = R/Z is the circle group.
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