Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657583 | Topology | 2009 | 11 Pages |
Abstract
Given an ordinal αα and a pointed topological space XX, we endow X<α=∪{Xβ:β<α}X<α=∪{Xβ:β<α} with the strongest topology that coincides with the product topology on every subset XβXβ of X<αX<α, β<αβ<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<αX<α for X=I,RX=I,R. This paper deals with some topological properties of spaces X<αX<α. Some new classification and characterization theorems are proved for these spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
T. Banakh, O. Shabat, M. Zarichnyi,