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Programming chaotic centers for shaping light branching in topological nematic vortices. [PDF]
Sci AdvYu X +7 more
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Structured coherent thermal emission from non-Hermitian metasurfaces. [PDF]
Nat CommunSun K +6 more
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Canadian Journal of Mathematics, 1980
Let G be a closed subgroup of one of the classical compact groups 0(n), U(n), Sp(n). By a reflection we mean a matrix in one of these groups which is conjugate to the diagonal matrix diag (–1, 1, …, 1). We say that G is a topological reflection group (t.r.g.) if the subgroup of G generated by all reflections in G is dense in G.It was shown recently by ...
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Let G be a closed subgroup of one of the classical compact groups 0(n), U(n), Sp(n). By a reflection we mean a matrix in one of these groups which is conjugate to the diagonal matrix diag (–1, 1, …, 1). We say that G is a topological reflection group (t.r.g.) if the subgroup of G generated by all reflections in G is dense in G.It was shown recently by ...
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-topological groups and its level L-topological groups
Fuzzy Sets and Systems, 2007Let \(X\) be a group. The authors show that an \(I(L)\)-topology on \(X\) compatible with the group structure is essentially a \([0,1)\)-indexed chain of \(L\)-topologies on \(X\) compatible with the group structure.
Zhang, Hua-Peng, Fang, Jin-Xuan
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Subgroups of Free Topological Groups and Free Topological Products of Topological Groups
Journal of the London Mathematical Society, 1975Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9].
Brown, R., Hardy, J. P. L.
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Proceedings of the American Mathematical Society, 1976
A locally compact topological group G is called (C4) if the group of inner automorphisms of G is closed in the group of all bicontinuous automorphisms of G. We show that each non-(C4) locally compact connect- ed group G can be written as a semidirect product of a (C A) locally compact connected group by a vector group.
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A locally compact topological group G is called (C4) if the group of inner automorphisms of G is closed in the group of all bicontinuous automorphisms of G. We show that each non-(C4) locally compact connect- ed group G can be written as a semidirect product of a (C A) locally compact connected group by a vector group.
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The Topology of Free Topological Groups
Journal of Mathematical Sciences, 2005This paper deals with the notion of the free topological group \(F(X)\) in the sense of Markov and with the topological Abelian group \(A(X)\) which is generated by a Tikhonov space \(X\). A variety of results is presented to demonstrate how useful explicit descriptions of the topologies on these groups are.
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