We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...

Consider a real n-plane bundle ξ with Euclidean metric. Associated to ξ are a number of auxiliary bundles: disc bundle, sphere bundle, projective bundle, k-frame bundle, etc. Here “bundle” simply means a local product with the indicated fibre. In each case one can show, by easy but repetitive arguments, that the projection map in question is indeed a local product; furthermore, the transition f...

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a “cohomology theory” for complex algebraic varieties. The theory is bigraded, functorial, and admits Gysin maps. It carries a natural cup product and a pairing to L-homology. Chern classes of algebraic bundles are defined in the theory. There is a na...

In this article I consider the convergence of the Eilenberg– Moore spectral sequence for Morava K-theory. This spectral sequence can be constructed by applying Morava K-theory to D. L. Rector’s geometric cobar construction of the Eilenberg–Moore spectral sequence. I have shown that the Eilenberg–Moore spectral sequence for Morava Ktheory converges if the Eilenberg–Moore spectral sequence for or...

We investigate the category of Eilenberg-Moore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through convex partitions of the space of all probability measures. Examples are investigated, and it is shown that finite spaces usually do not have algebras at all.

Suppose F is a special Gamma-space equipped with natural transformation to the infinite symmetric power functor. Segal's loop space machine associates spectrum, denoted kF, map integral Eilenberg-Mac Lane spectrum. In our previous work we constructed filtration of kF by sequence spectra, which called "stable rank F". this paper give new construction stable filtration. The combinatorial in natur...

We exhibit a two-dimensional, acyclic, Eilenberg–Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π1(X) coincides, up to homotopy, with the W -nullification of X; that is, the natural map X → X+ is homotopy initial among maps X → Y where the based mapping space map∗(W,Y ) is weakly contractible. Furthermore, we describe the ...

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW -complex to the classifying space of a crossed module and also, ...