1. ip is real-analytic; 2. the rank of <p equals p on an everywhere dense subset of U; 3. (f(U) is closed in V; 4. for each compact subset K C <p(U), there exists a compact subset H C U such that <p(H) = K. Then the composition subalgebra A? = {foip: f e C°°(V)} is closed in C°°(U), when this algebra carries its natural Frechet topology (convergence on compact subsets of the function and all it...

The aim of the present paper is to prove the following result: Let (#t)t>0 be a vaguely cont inuous convolut ion semigroup consisting of symmetric probabil i ty measures on a locally compact abelian group G. Then there exists a closed subgroup H of G such that supp (#t) = H for all t > 0. As a consequence of this result we get that the support of a symmetric infinitely divisible distribution in...

LetH be a Hilbert space, L(H) the algebra of all bounded linear operators onH and 〈, 〉A : H ×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉 , ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = QA} for different choices...

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [C-S1] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariant for simply connected manifolds in the following sense. Let f : M1 → M2 be a homotopy equivalence of simply connected cl...

We give an example of a exible curve, i.e., a closed curve ? so that for any other closed curve ? 0 and " > 0 there is a homeomorphism of the sphere, conformal oo ?, so that (?) lies in an " neighborhood of ? 0. Moreover, for any guage function h such that h(t) = o(t) as t ! 0, we may take ? to have zero Hausdorr measure with respect to h. This extends a result of Robert Kaufman on removable se...

We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [4] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariants in the following sense. Let f : M1 → M2 be a homotopy equivalence of closed, oriented n-manifolds. Then the induced equiv...

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [3] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariants in the following sense. Let f : M1 → M2 be a homotopy equivalence of closed, oriented n-manifolds. Then the induced equiv...

The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f : N → M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h : N → M such that h an...