Using specializations of unfold and fold on a generic tree data type we derive unranking and ranking functions providing natural number encodings for various Hereditarily Finite datatypes. In this context, we interpret unranking operations as instances of a generic anamorphism and ranking operations as instances of the corresponding catamorphism. Starting with Ackerman’s Encoding from Hereditar...

A continuum means a compact connected metric space. For a positive integer n, a continuum X is said to be n-equivalent provided that X contains exactlyn topologically distinct subcontinua. A continuumX is said to be hereditarily n-equivalent provided that each nondegenerate subcontinuum of X is n-equivalent. If there exists a positive integer n such that X is n-equivalent, then X is said to be ...

In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.

Lozzio et al,(1,2) reported on the successful transplantation of human myelogenous leukemic cells by the use of the hereditarily asplenic-athymic (Lasat) mouse produced by mating the congenitally asplenic mouse impaired of its antibody production and the hereditarily athymic mouse deficient of its cellular immunity. On the other hand, we(3) reported hereditarily asplenic-athymic mouse by mating...

We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99

We prove that every chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. In particular, it follows that there exists a finite-to-one map from a hereditarily indecomposable continuum (the pseudoarc) onto hereditarily decomposable continuum. This answers a question by J. Krasinkiewicz.