Additive structure of multiplicative subgroups of fields and Galois theory.

Mahé, Louis; Mináč, Ján; Smith, Tara L.

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Noncommutative Valdivia compacta

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We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space $K$ , we show that $K$ is Corson if and only if every continuous...

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Continuing the idea of Part I, we deal with more involved pseudogroup of transformations $\bar{x} = ϕ (x)$ , $\bar{y} = L (x) y$ , $\bar{z} = M (x) z, ...$ applied to the first order differential equations including the underdetermined case (i.e. the Monge equation $y^{'} = f (x, y, z, z^{'})$ ) and certain differential equations with deviation (if $z = y (ξ (x))$ is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction...