Consider the set of Borel probability measures on Rk and endow it with topology weak convergence. We show that subset all which belong to domain attraction some multivariate extreme value distributions is dense first Baire category. In addition, analogue result holds in context free theory.

For a ring R, Hilbert’s Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. We consider computability of this set for subrings R of the rationals. Applying Baire category theory to these subrings, which naturally form a topological space, relates their sets HTP(R) to the set HTP(Q), whose decidability remains an open question. The main resu...

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space X, showing that these groups do not admit a compatible Polish group topology and, in the case of Z-actions, are coanalytic nonBorel inside Homeo(X). We point out that the full group of a minimal homeomorphism is topologically simple. We also study some properties of the closure of the full group of a...

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

where F is a Hausdorff continuous multifunction with closed, bounded values. In this paper we prove the local existence of a solution of (1.1 ), assuming that the convex closure of F(x,,) has finite codimension. More precisely, we assume the existence of a closed affine subspace E, G E with finite codimension, such that the interior of E. n E6 F(x,) relative to E,, is nonempty. Two special case...

We prove a theorem of Steel that solves the 12th Delfino Problem. We build on the one hand on a lemma of Woodin on universally Baire sets and their projections in certain generic extensions in the presence of strong cardinals; on the other hand we use certain premice to find projective uniformizations of projective sets.

Abstract We introduce the notions of ? -Baire property and -semiopen set using sets Lebesgue measure zero. For a family A subsets real line, we define ( ? )-property analogously as it was done in category case for )-property. The main result is that all line having has iff situated between Euclidean topology sets.