A generalization of the Levin-Rubin-Schapiro Factorization Theorem

作者：Virk Ziga^*

来源：Topology and Its Applications, 2012, 159(3): 695-703.

DOI：10.1016/j.topol.2011.10.018

• Dimension theory
• Mardesic factorization
• Inverse limits

Given a map f : X -%26gt; Y of compact Hausdorff spaces, the Mardesic Factorization Theorem provides us a factorization f = qj, j : X -%26gt; Z, q : Z -%26gt; Y through a compact Hausdorff space Z with dim Z %26lt;= dim X and weight of Z being at most weight of Y. The theorem has been generalized several times in various contexts with the Levin-Rubin-Schapiro Factorization Theorem being one of the most notable developments. %26lt;br%26gt;This paper introduces a new generalization in which the factoring space Z inherits the extension property for every map in the spirit of the Levin-Rubin-Schapiro Factorization Theorem. Such inheritance of extension properties is expressed by a new notion of extensional equivalence. Furthermore, we study the impact of such a generalization on the extension relation between maps, f tau i.

• 出版日期2012-2-15