On the algebraic dimension of Riesz spaces
Keyword(s):
We prove that the algebraic dimension of an infinite dimensional $C$-$\sigma$-complete Riesz space (in particular, of a Dedekind $\sigma$-complete and a laterally $\sigma$-complete Riesz space) with the principal projection property which either has a weak order unit or is not purely atomic, is at least continuum. A similar (incomparable to ours) result for complete metric linear spaces is well known.
1988 ◽
Vol 104
(2)
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pp. 331-345
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Keyword(s):
1983 ◽
Vol 35
(6)
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pp. 1010-1029
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Keyword(s):
1989 ◽
Vol 105
(3)
◽
pp. 523-536
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2011 ◽
Vol 9
(3)
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pp. 283-304
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Keyword(s):
Keyword(s):