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F σ -mappings and the invariance of absolute Borel classes

Petr Holický, Jiří Spurný (2004)

Fundamenta Mathematicae

It is proved that F σ -mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any F σ -mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable F σ -set X X satisfying f ( X ) = Y .

Filippov Lemma for certain second order differential inclusions

Grzegorz Bartuzel, Andrzej Fryszkowski (2012)

Open Mathematics

In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1...

Finite Product of Semiring of Sets

Roland Coghetto (2015)

Formalized Mathematics

We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].

Frame monomorphisms and a feature of the l -group of Baire functions on a topological space

Richard N. Ball, Anthony W. Hager (2013)

Commentationes Mathematicae Universitatis Carolinae

“The kernel functor” W k LFrm from the category W of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In W , monics are one-to-one, but not necessarily so in LFrm. An embedding ϕ W for which k ϕ is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The W -objects every embedding of which is KI are characterized;...

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