Multisequences

Abstract

This paper is essentially an introduction to, and a survey of multisequences, but also it contains some new concepts and results. Multisequences are maps from the sets of maximal elements of some special trees. They find application in numerous problems related to sequentiality, like characterizations of sequential and subsequential spaces, preservation of sequentiality and of Fréchetness by various operations, estimates of sequential order of products.

Keywords: multisequence, sequential cascade

Quaestiones Mathematicae 29(2006), 239–277