Locally flat embeddings of Hilbert cubes are flat
Shapes of finite-dimensional compacta
On some applications of infinite-dimensional manifolds to the theory of shape
A general approximation theorem for Hilbert cube manifolds
Homotopic homeomorphisms of infinite-dimensional manifolds
On the structure of Hilbert cube manifolds
On delta sets and their realizable subsets in Krull monoids with cyclic class groups
Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question of determining...
On the arithmetic of arithmetical congruence monoids
Let ℕ represent the positive integers and ℕ₀ the non-negative integers. If b ∈ ℕ and Γ is a multiplicatively closed subset of , then the set is a multiplicative submonoid of ℕ known as a congruence monoid. An arithmetical congruence monoid (or ACM) is a congruence monoid where Γ = ā consists of a single element. If is an ACM, then we represent it with the notation M(a,b) = (a + bℕ₀) ∪ 1, where a, b ∈ ℕ and a² ≡ a (mod b). A classical 1954 result of James and Niven implies that the only ACM...
On the Delta set of a singular arithmetical congruence monoid
If and are positive integers with and , then the set
is a multiplicative monoid known as an arithmetical congruence monoid (or ACM). For any monoid with units and any we say that is a
Elasticity in certain block monoids via the Euclidean table
Fibering Hilbert cube manifolds over ANRs
A characterization of minimal zero-sequences of index one in finite cyclic groups.
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