In this paper we prove a cardinal inequality for supercompact Uausdorff spaces which gives insight into the cellular structure of such spaces and yields new examples of compact Uausdorff non-supercompact spaces.

In this paper we consider the construction of a norm-continuous index theory for unitary equivalence up to commutative normality of operators on a separable Jlilhert space, and establish some essentially best possible results in this direction for operators which can be written as direct sums of weighted shifts and normal operators. Indeed, for such operators we establish both a normcontinuous analogue and a norm-continuous extension of the elegant results of L. Brown, R. Douglas and P. Fillmore [4].

We denote by 5 the class of functions, f(z), that are analytic and univalent in U = ﹛z: |z| < 1﹜ and have the normalization

All spaces in this paper will be separable and metric. A closed embedding i: M → TV is said to be locally flat (of codimension n) if for each x0 ∈ M there is an open set U in M containing xo and an open embedding h: U X Rn → N for which h(x, 0) = i(x), for all x ∈ U.

Let

denote the Nth Fermat curve. The period lattice of F(N) is contained with finite index in the product of certain lattices Lr,s (see [6]), and to this inclusion of lattices there corresponds an isogeny of the Jacobian of F(N) onto a product of abelian varieties. The purpose of this paper is to determine when two factors in this product are isogenous over C, and whether they are absolutely simple.

We shall assume throughout this paper, unless otherwise specified, that p is a fixed number, 1 < p < ∞.

It is well known that to prove the poin.twise ergodic convergence of a contraction T on an Lp-space it is enough to prove a Dominated Ergodic Estimate (DEE) for T (see e.g. [11]).

This note addresses the question of characterizing the elements of a C*-algebra which have local unitary cross sections in the sense described below. Let denote a C*-algebra with identity and let denote the unitary group in .

If UR is a real subspace of a finite dimensional vector space VC over the field C of complex numbers, then there exists a basis ﹛e1, … , en﹜ of VG such that

Notation. For S a subset of the extended plane C* = C ∪ (∞ ) let S0 be its interior, its closure in C* and its boundary. H(S) and M(S) will denote the sets of all restrictions to S of functions which are, on a neighborhood of S, holomorphic or meromorphic, respectively. A (S) will stand for the set of functions from S to C* which are continuous on S and whose restriction to S° are holomorphic.

There are three lattice-theoretic properties that are generally used to open a discussion on sublattices of a free lattice:

(W) for all a, b, c, d, a Λ b ≦ c V d implies a A b ≦ c, a Λ b g rf, a ≦cVd,orb ≦ c V d;

(SDv) for all a, b, c, a V b = a V c implies a V b = a V (b Λ c ) ;

(SDΛ) for all a, b, c, a Λ b = a Λ c implies a Λ b = a Λ (b V c).

We investigate the extent to which knot groups determine knot manifolds and knot types. Let Ki(i = 1, 2) denote a tame knot in S3, let Ci denote a Ki-knot manifold, and assume that Π1(C1) ≈ Π1(C2). The first named author recently showed (in [6]) that, if C1 has no essential annulus, then C1 ≅ C2, and so K1 and K2 are equivalent, if K1 has property P.

The first example of a nuclear Fréchet space without a basis was given by B. S. Mitiagin and N. M. Zobin [9; 10]. The question of existence of subspaces without bases in nuclear Fréchet spaces was recently settled in papers by P. Djakov and B. S. Mitiagin [2] and Ed Dubinsky [5]. In this paper we consider the analogous question for quotient spaces. As in the case of subspaces we obtain a complete solution to the problem.

σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.

Let D be an integral domain with 1 ≠ 0 . We consider “property SP” in D, which is that every ideal is a product of semiprime ideals. (A semiprime ideal is equal to its radical.) It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. We prove that a domain D with property SP is almost Dedekind, and we give an example of a nonnoetherian almost Dedekind domain with property SP.

Let π: X’ —” X be a double cover of 2n-dimensional Poincaré duality (PD) spaces. The double cover is a fibering so it is classified by a map f: X → RP1+1(l ≫ n). If the homotopy class of f contains a representative which is Poincaré transverse [5] to RPl ⊂ RPl+1, we say that w is Poincarésplit-table.

Definition. [1] A base B for the topology of a space S is centered provided every perfectly decreasing filterbase F in B is regular and either F is free or F converges. A centered base which contains no free perfectly decreasing filterbase is said to be complete.

In this paper we study the Lie algebra of derivations of the exterior algebra of a vector space V over a field K of characteristic ≠ 2, and the group A of automorphisms of .

A ring with involution R is an associative ring endowed with an antiautomorphism * of period 2. One of the first commutativity results for rings with * is a theorem of S. Montgomery asserting that if R is a prime ring, in which every symmetric element s = s* is of the form s — sn(s) (n(s) ≧ 2), then either R is commutative or R is the 2 X 2 matrices over a field, which is a nice generalization of a well-known theorem of N. Jacobson on rings all of whose elements x = xn(x).