A universal model infinite-dimensional space

Abstract

Given an ordinal α and a pointed topological space X , we endow X < α = ∪ { X β : β < α } with the strongest topology that coincides with the product topology on every subset X β of X < α , β < α . It turns out that many important model spaces of infinite-dimensional topology (including the topology of non-metrizable manifolds) can be obtained as spaces of the form X < α for X = I , R . This paper deals with some topological properties of spaces X < α . Some new classification and characterization theorems are proved for these spaces.