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The first probe of the correlation of the T-odd one-particle fragmentationfunction responsible for the left--right asymmetry of fragmentation of atransversely polarized quark is done by using the 1991-95 DELPHI data for $Z\to2$-jet decay. Integrated over the fraction of longitudinal and transversalmomenta, this correlation is of 1.5% order, which means order of 13% for theanalyzing power.  A rather large ($\approx 10%$) handedness transversal to the production planewas observed in the diffractive production of ($\pi^-\pi^+\pi^-$) triples fromnuclei by the $40 GeV/c \pi^-$--beam. It was shown that the phenomenon has aclear dynamic origin and resembles the single spin asymmetry behavior. All thismakes us hope to use this effects in polarized DIS experiments for transversitymeasurement.Comment: 10 pp, 5 epsfig, Latex 2e, szjp.cls, epsfig.sty, wrapfig.sty  included. Talk in "Spin and Symmetry - Praha98". To be published in  Czechoslovak Journal of Physics, Supp

On the T-old quark fragmentation function and on transversal handedness