Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

Let X be a Riemann surface equipped with a projective structure (i.e., a covering by coordinate charts such that the transition functions are of the form z 7−→ (az + b)/(cz + d)). Let L be a line bundle on X such that L = TX . Let J (L) −→ X denote the jet bundle of order m for the line bundle L. For i ≥ j, there is a natural restriction homomorphism from J (L) onto J (L). We prove that for any...

Suppose L is a semisimple Levi subgroup of a connected Lie group G, X is a Borel G-space with finite invariant measure, and α : X × G → GLn(R) is a Borel cocycle. Assume L has finite center, and that the real rank of every simple factor of L is at least two. We show that if L is ergodic on X, and the restriction of α to X × L is cohomologous to a homomorphism (modulo a compact group), then, aft...

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

One reason for changing the representation of a game is to make it similar to a previously solved one. As a def in i t ion of s im i la r i t y , people have previously often proposed homomorphism-like structures. One such structure, the "s -homomorphism", is defined and studied in this paper. It is indicated that a useful winning s t rategy exists for any game in a general class cal led, "posi...

We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minor-closed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletion-contraction identity, F (M) = δeF (M r e) + γeF (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the ...