논문KCI 등재
Reflexive Index of a Family of Sets
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As a further study on reflexive families of subsets, we introduce the reflexive index for a family of subsets of a given set and show that the index of a finite family of subsets of a finite or countably infinite set is always finite. The reflexive indices of some special families are also considered.
Abstract
As a further study on reflexive families of subsets, we introduce the reflexive index for a family of subsets of a given set and show that the index of a finite family of subsets of a finite or countably infinite set is always finite. The reflexive indices of some special families are also considered.
참고문헌 (9)
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- W. E. Longstaff, "Strongly Reflexive subspace lattices", J. London Math. Soc., 11(2), pp.491~498 (1975)
- 4W. E. Longstaff, "On lattices whose every realization on Hilbert space is Reflexive", J. London Math. Soc., 37(2), pp.499~508 (1988)
- W. E. Longstaff, "On the ranks of single elements of Reflexive operator algebras", Proc. Amer. Math. Soc., 125(10), pp.2875~2882 (1997)
- Z. Yang, "Reflexive families of closed sets", Fund. Math., 192, pp.111~120 (2006)
- Z. Yang, "On Reflexive closed set lattices", Comment. Math. Univ. Carolinae, 51(1), pp.23~32 (2010)
- D. Zhao, "On Reflexive subobject lattices and Reflexive endomorphism algebras", Com-ment. Math. Univ. Carolinae, 44, pp.23~32 (2003)
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