Vol. 32, No. 1, 1970

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Concerning semi-stratifiable spaces

Geoffrey David Downs Creede

Vol. 32 (1970), No. 1, 47–54

In this paper, a class of spaces, called semi-stratifiable spaces is introduced. This class of spaces lies between the class of semi-metric spaces and the class of spaces in which closed sets are Gδ. This class of spaces is invariant with respect to taking countable products, closed maps, and closed unions. In a semi-stratifiable space, bicompactness and countable compactness are equivalent properties. A semi-stratifiable space is Fσ-screenable.

A T1-space is semi-metric if and only if it is semi-stratifiable and first countable. A completely regular space is a Moore space if and only if it is a semi-stratifiable p-space.

Mathematical Subject Classification
Primary: 54.20
Received: 17 March 1969
Published: 1 January 1970
Geoffrey David Downs Creede