Abstract
Properties of C1 smooth skew products of maps of an interval with stable as a whole family of fibers maps are established. These results are applied to the proof of the criterion of Ω-stability of C1-smooth skew products of maps of an interval (with respect to homeomorphisms of skew products class).The proper subspace of the space of C1smooth skew products of maps of an interval is distinguished, where Ω-stable C1smooth skew products are contained. It is proved that Ω- stable skew products are not dense in the distinguished subspace of C1 -smooth maps.
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