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In this paper by using of semi-bornnology the notion of semibornological attractors for semi-dynamical systems is studied. It is proved that: this concept of attractor is invariant up to a special kind of lower semicontinuous multifunctions. Attractors for semi-dynamical systems on vectorical spaces are studied. The notion of semi-bornological stability is presented. It is proved that: the semi-bornological conjugacy preserves attractor. The notion of chaotic multifunction is considered.