On hyperspaces of generalized metric spaces
by
Boualem Alleche
University of Rouen

Our work is in order to complete the study of the heredity of the classes of generalized metric spaces to the hyperspaces of non-empty compact subsets and finite subsets with the finite (Vietoris) topology.

It is well known that metrizability, and most of separation axioms of a space, including regularity and T₂-ness, are inherited to such hyperspaces. Takemi Mizokami, recently studied the heredity of other notions of generalized metric spaces and answered positively the case of Moore spaces. We will study this problem for new notions of generalized metric spaces, namely, weakly developable spaces, weakly k-developable spaces, and spaces with a sharp base, introduced recently by A. Arhangelskii, J. Calbrix, and myself.

We also present some results obtained with A. Amara on the first-countability and the Fréchet-Urysohn property of the cocompact topology, generalizing the old ones obtained by C. Costantini and P. Vitolo.

Date received: August 6, 1998