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Orthomodular generalizations of homogeneous Boolean algebras

Published online by Cambridge University Press:  09 April 2009

C. H. Randall ,
M. F. Janowitz  and
D. J. Foulis
C. H. Randall
Affiliation:
University of MassachusettsAmherst, MA 01002, USA
M. F. Janowitz
Affiliation:
University of MassachusettsAmherst, MA 01002, USA
D. J. Foulis
Affiliation:
University of MassachusettsAmherst, MA 01002, USA
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It is well known that the so-called reduced Borel algebra, that is, the Boolean algebra of all Borel subsets of the unit interval modulo the meager Borel sets of this interval, can be abstractly characterized as a complete, totally non-atomic Boolean algebra containing a countable join dense subset. (For an indication of the history of this result, see, for example, ([2], p. 483, footnote 12.) From this characterization, it easily follows that the reduced Borel algebra B is “homogeneous” in the sense that every non-trivial in B is isomorphic to B.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 94 - 104
Copyright
Copyright © Australian Mathematical Society 1973

References

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