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Article

Wójtowicz, Marek
An elementary proof of a theorem on sublattices of finite codimension. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 39 (1998), issue 1, pp. 99-100
MSC: 46A40, 47B65 | MR 1622986 | Zbl 0937.46002
Keywords:
linear lattice; Lebesgue property; lattice homomorphism
Summary:
This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property.
References:
[1] Abramovich Y.A., Lipecki Z.: On ideals and sublattices in linear lattices and $F$-lattices. Math. Proc. Cambridge Phil. Soc. 108 (1990), 79-87. MR 1049761 | Zbl 0751.46009
[2] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces. Academic Press, 1978. MR 0493242 | Zbl 1043.46003
[3] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I. North-Holland, 1971.
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