An approach to shape covering maps (Q1974108)

The homotopy concepts of a ``covering map'' and a ``fibration'' are studied in shape theory by many authors [\textit{S. Mardešić} and \textit{J. Segal}, Shape theory (1982; Zbl 0495.55001)] for historical developments and related references. This paper provides an approach to shape covering maps which is naturally allied to the concept of *-fibration introduced by \textit{S. Mardešić} and \textit{T. B. Rushing} [General Topol. Appl. 9, 193-215 (1978; Zbl 0398.55011)]. More specifically, it is proved that every shape covering map is a *-fibration. This notion of shape covering maps appears to be quite useful since it preserves many useful properties of covering maps.