Bulletin of the Australian Mathematical Society
- Bulletin of the Australian Mathematical Society / Volume 7 / Issue 03 / December 1972, pp 353-358
- Copyright © Australian Mathematical Society 1972
- DOI: http://dx.doi.org/10.1017/S0004972700045196 (About DOI), Published online: 17 April 2009
Research Article
Transversals of squares
N.H. Williamsa1
a1 Department of Mathematics, Monash University, Clayton, Victoria.
Abstract
Let κ and λ be cardinal numbers. Take any family A = {Aν; ν 
N} where each Aν is a product Aν = Bν x Cν with |Bν = |Cν| = Nα, such that if B x C 
Aμ x Aν (for μ ≠ ν) then |B|, |c| < λ. We investigate under what conditions on α, κ, λ and |N| there will be a set T with 1 ≤ |T
Aν| < κ for each ν.
(Received June 05 1972)
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