Representation of Group Isomorphisms: The Compact Case
Keyword(s):
LetGbe a discrete group and letAandBbe two subgroups ofG-valued continuous functions defined on two 0-dimensional compact spacesXandY. A group isomorphismHdefined betweenAandBis calledseparatingwhen, for each pair of mapsf, g∈Asatisfying thatf-1eG∪g-1eG=X, it holds thatHf-1eG∪Hg-1eG=Y. We prove that under some mild conditions every biseparating isomorphismH:A→Bcan be represented by means of a continuous functionh:Y→Xas a weighted composition operator. As a consequence we establish the equivalence of two subgroups of continuous functions if there is a biseparating isomorphism defined between them.
2003 ◽
Vol 2003
(72)
◽
pp. 4547-4555
Keyword(s):
2004 ◽
Vol 2004
(71)
◽
pp. 3941-3950
2014 ◽
Vol 279
(1-2)
◽
pp. 423-434
◽
Keyword(s):