A chain compact space which is not strongly scattered

A compactT ₂ spaceX which is separable, scattered and uncountable, but still so thatX ^α−X^α+1is countable for all α∈[1, ω) is constructed. This answers one of the problems presented by M. E. Rudin in a conference as an open problem and attributed by her to Telgarsky. The author acknowledges a faculty research grant from Memphis State University when this paper was written.     

Einstein metrics on compact Lie groups which are not naturally reductive

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by D??Atri and Ziller (Mem Am Math Soc 18, (215) 1979). In 1996 the second author obtained non-naturally reductive Einstein metrics on the Lie group SU(n) for n ??? 6, by using a method of Riemannian submersions. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) (n ??? 11), Sp(n) (n ??? 3), E ₆, E ₇, and E ₈.     

On Banach spaces whose dual balls are not weak∗ sequentially compact

Theorem 1. LetX be a Banach space. (a) IfX ^∗ has a closed subspace in which no normalized sequence converges weak^∗ to zero, thenl ₁ is isomorphic to a subspace ofX. (b) IfX ^∗ contains a bounded sequence which has no weak^∗ convergent subsequence, thenX contains a separable subspace whose dual is not separable. The second-named author was supported in part by NSF-MPS 72-04634-A03.     

The reconstruction conjecture is true if all 2-connected graphs are reconstructible

It is shown that the Reconstruction Conjecture is true for all finite graphs if it is true for the 2-connected ones.     

A pseudocompact meta-lindeöf space which is not compact

We construct a pseudocompact meta-Lindelöf space which is not compact. This contrasts with the results that pseudocompact metacompact spaces are compact (Scott, Forster, Watson) and that pseudocompact para-Lindelöf spaces are compact (Burke, Davis). The space is completely regular and has a point-countable base.     

Examples of compact holomorphic symplectic manifolds which are not Kählerian II

Oblatum 28-VII_1993 & 15-II-1995     

The nucleolus is not aggregate-monotonic on the domain of convex games

We show that the nucleolus is not aggregate-monotonic on the domain of convex games, and that this lack of monotonicity holds even if there are as few as four agents. Received May 1999/Revised version December 1999     

Many homotopy categories are homotopy categories

We show that any category that is enriched, tensored, and cotensored over the category of compactly generated weak Hausdorff spaces, and that satisfies an additional hypothesis concerning the behavior of colimits of sequences of cofibrations, admits a Quillen closed model structure in which the weak equivalences are the homotopy equivalences. The fibrations are the Hurewicz fibrations and the cofibrations are a subclass of the Hurewicz cofibrations. This result applies to various categories of spaces, unbased or based, categories of prespectra and spectra in the sense of Lewis and May, the categories of L-spectra and S-modules of Elmendorf, Kriz, Mandell and May, and the equivariant analogues of all the afore-mentioned categories.     

Valdivia compact groups are products

It is shown that every Valdivia compact group is homeomorphic to a product of metrizable compacta.     

ACCP Rises to the Polynomial Ring if the Ring has Only Finitely Many Associated Primes

Abstract

We show for a commutative ring R with unity: If R satisfies the ascending chain condition on principal ideals (accp) and has only finitely many associated primes, then for any set of indeterminates X the polynomial ring R[X] also satisfies accp. Further we show that accp rises to the power series ring R[[X]] if R satisfies accp and the ascending chain condition on annihilators.     

Bernoullis are standard when entropy is not an obstruction

In this paper we look atr equivalence, which is an equivalence relation that is implicit in Vershik's classification ofr-adic decreasing sequences of σ-algebras, and also in work of Stepin. this equivalence relation is used to classify group actions of the group It is shown that given any sequence of natural numbers satisfying a certain growth rate, all BernoulliG actions arer equivalent to a certain natural action ofG, which we call the translation action. Furthermore, these actions are zeror entropy andr finitely determined, where this notion arises canonically from the restricted orbit equivalence theory of Kammeyer and Rudolph.     

Topological and fractal properties of real numbers which are not normal

The set L of essentially non-normal numbers of the unit interval (i.e., the set of real numbers having no asymptotic frequencies of all digits in their nonterminating s-adic expansion) is studied in details. It is proven that the set L is generic in the topological sense (it is of the second Baire category) as well as in the sense of fractal geometry (L is a superfractal set, i.e., the Hausdorff-Besicovitch dimension of the set L is equal 1). These results are substantial generalizations of the previous results of the two latter authors [M. Pratsiovytyi, G. Torbin, Ukrainian Math. J. 47 (7) (1995) 971-975].The Q^∗-representation of real numbers (which is a generalization of the s-adic expansion) is also studied. This representation is determined by the stochastic matrix Q^∗. We prove the existence of such a Q^∗-representation that almost all (in the sense of Lebesgue measure) real numbers have no asymptotic frequency of all digits. In the case where the matrix Q^∗ has additional asymptotic properties, the Hausdorff-Besicovitch dimension of the set of numbers with prescribed asymptotic properties of their digits is determined (this is a generalization of the Eggleston-Besicovitch theorem). The connections between the notions of “normality of numbers” respectively of “asymptotic frequencies” of their digits is also studied.     

Testing the hypothesis of preservation of the properties of a normal linear model if the possible change point is known

Tests are proposed for the hypothesis of the preservation of the linear normal model in the case, where the possible change point is known. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 86–95, Perm, 1991.