The purpose of this
paper is to introduce a new class of spaces, called linearly stratifiable spaces,
which contains the class of stratifiable spaces and is contained in the class of
hereditarily paracompact spaces. The notion of linearly stratifiable spaces is
related to several of the concepts most recently studied by the late Professor
Hisahiro Tamano, and also to questions raised by A. H. Stone and E. A.
Michael concerning the normality and paracompactness of certain product
spaces.