Glasnik Matematicki, Vol. 50, No. 1 (2015), 233-243.

FACTORIZATION OF UNIFORMLY CONTINUOUS MAPS THROUGH UNIFORM SHAPE FIBRATIONS

Takahisa Miyata

Department of Mathematics and Informatics, Graduate School of Human Development and Environment, Kobe University, 3-11 Tsurukabuto, Nada-Ku, Kobe, 657-8501 Japan
e-mail: tmiyata@kobe-u.ac.jp


Abstract.   It is well-known that every continuous map is the composite of a homotopy equivalence and a fibration. In this paper, we introduce the notion of uniform shape fibration, and show that every uniformly continuous map is the composite of a uniform shape equivalence and a uniform shape fibration.

2010 Mathematics Subject Classification.   55P55, 54E15.

Key words and phrases.   Uniform shape fibration, uniform homotopy lifting property, factorization axiom.


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DOI: 10.3336/gm.50.1.14


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