A note on Riesz spaces with property-b

Alpay, S.
Altin, B.
Tonyali, C.
We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.


A generalisation of the Morse inequalities
Bhupal, Mohan Lal (Cambridge University Press (CUP), 2001-06-01)
In this paper we construct a family of variational families for a Legendrian embedding, into the 1-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embeddings, by discretising the action functional. We compute the second variation of a generating function obtained as above at a nondegenerate critical point and prove a formula relating the signature of the second variation to the Maslov index as the mesh goes to zero. We use this to prove a generalisation of the ...
Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
An observation on realcompact spaces
Ercan, Z (American Mathematical Society (AMS), 2006-01-01)
We give a characterization of realcompact spaces in terms of nets. By using the technique of this characterization we give easy proofs of the Tychonoff Theorem and the Alaoglu Theorem.
A remark on CD0(K)-spaces
Alpay, S.; Ercan, Z. (Springer Science and Business Media LLC, 2006-05-01)
A representation of the CDo (K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points.
Citation Formats
S. Alpay, B. Altin, and C. Tonyali, “A note on Riesz spaces with property-b,” CZECHOSLOVAK MATHEMATICAL JOURNAL, pp. 765–772, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66850.