Vol. 56, No. 1, 1975

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Intermediate Riesz spaces

Joseph E. Quinn

Vol. 56 (1975), No. 1, 225–263

A Riesz space E will be defined to be intermediate with respect to the Riesz space L if L can be embedded in E as a Riesz subspace L in such a way that the elements of E are both the infimum and the supremum of elements in L#. The main objectives of this paper are to investigate the extendability of certain order convergence properties from a Riesz space to its intermediate spaces and to compare the prime ideal structure of a Riesz space to the prime ideal structure of its intermediate spaces.

Mathematical Subject Classification 2000
Primary: 46A40
Secondary: 06A65
Received: 22 July 1973
Revised: 18 April 1974
Published: 1 January 1975
Joseph E. Quinn