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P3BD-closed sets

✍ Scribed by Junling Zhou; Yanxun Chang

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
150 KB
Volume
19
Category
Article
ISSN
1063-8539

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✦ Synopsis

A concept called P3BD-closed set is introduced to describe a set of positive integers which is both PBD-closed and 3BD-closed. The theory of P3BD-closure is developed and a few examples of P3BD-closed sets are exhibited. In the process, the existence spectrum of OLIQ s (overlarge sets of idempotent quasigroups with their own idempotent orthogonal mates) is almost determined. A pair of orthogonal OLIQ s is shown to asymptotically exist. The existence of OLIQ * s (overlarge sets of idempotent quasigroups with their own orthogonal mates not necessarily specifying idempotency) is also established with only 10 possible exceptions remained.

πŸ“œ SIMILAR VOLUMES

On the 3BD-closed set B3({4,5,6})
On the 3BD-closed set B3({4,5,6})
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Let B 3 ðKÞ ¼ fv v v v : 9 9 an Sð3; K; v v v vÞg. For K ¼ f4g or f4; 6g, B 3 ðKÞ has been determined by Hanani, and for K ¼ f4; 5g by a previous paper of the author. In this paper, we investigate the case of ; 5; 6gÞ by Hanani and that B 3 ðf4; 5gÞ ¼ fv v v v > 0 : v v v v 1; 2; 4; 5; 8; 10 ðmod 1

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Let v, k be positive integers and k β‰₯ 3, then K k = {v : v β‰₯ k} is a 3-BD closed set. Two finite generating sets of 3-BD closed sets K 4 and K 5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v β‰₯ 6, then v ∈ B 3 (K, 1), where K = {6, 7, . . . , 41, 45

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We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop-compact.