This research demonstrates that T(3) implies T-k in well distributed sets, highlighting significant properties of transversal theorems.
We prove the colourful versions of three classical transversal theorems: The Katchalski-Lewis Theorem "T(3) implies T-k", the "T(3) implies T" Theorem for well distributed sets, and the Goodmann-Pollack Transversal Theorem for hyperplanes.
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Oliveros et al. (2008) studied this question.
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