The main purpose of this paper is to study the weight under hereditarily irreducible mappings between continua. The main result states that if f : X → Y is an hereditarily irreducible and surjective mapping of a D-continuum X, then w(X) = w(Y ).

In this paper we examine the role of the β-space property (equivalently of the MCM-property) in generalized ordered (GO-)spaces and, more generally, in monotonically normal spaces. We show that a GO-space is metrizable iff it is a β-space with a Gδ-diagonal and iff it is a quasidevelopable β-space. That last assertion is a corollary of a general theorem that any β-space with a σ-point-finite ba...

We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality א1. This can be used, together with a known combinatorial equivalent of the existence of a non-free Whitehead group, to prove that it is consistent that every Whitehead group is free but not every hereditarily separable group is free. We also show that the fact that Z is a p.i.d. with i...

The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a “localization” of the notion of hypercyclicity. In particular, let T be a bounded linear operator acting on a Banach space X and let x be a non-zero vector in X such that for every open neighborhood U ⊂ X of x and every non-empty open set V ⊂ X there exists a positive integer n such tha...

Prolog’s ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. ranking and unranking functions. Starting from a generalization of Ackerman’s encoding of Hereditarily Finite Sets with Urelements and a novel tupling/untupling operation, we derive encodings for Finite Functions and use them a...