Regular Lie groups and a theorem of Lie-Palais.
A correspondence between finite-dimensional Lie superalgebras and supergroups.
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
On a result of K. P. Hart about non-existence of measurable solutions to the discrete expectation maximization problem
It was shown that there is a statistical learning problem – a version of the expectation maximization (EMX) problem – whose consistency in a domain of cardinality continuum under the family of purely atomic probability measures and with finite hypotheses is equivalent to a version of the continuum hypothesis, and thus independent of ZFC. K. P. Hart had subsequently proved that no solution to the EMX problem can be Borel measurable with regard to an uncountable standard Borel structure on , and...
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
On Lie groups in varieties of topological groups
On a universality property of some abelian Polish groups
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
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