International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 477-482
On certain constactions in finitistic spaces
Department of Mathematics, University of Jammu, Jammu 180001, India
Received 23 April 1982; Revised 25 November 1982
Copyright © 1983 Satya Deo and Mohan Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Since the product of two finitistic spaces need not be finitistic, and also because a continuous closed image of a finitistic space need not be finitistic, it is natural to enquire whether or not the class of finitistic spaces in closed under the formation of cones, reduced cones, suspensions, reduced suspensions, adjunction spaces, mapping cylinders, mapping cones, joins and smash products. In this paper we prove that all of the above constructs, except joins and smash products, of finitistic spaces are finitistic. The joins and smash products of finitistic spaces, however, need not be finitistic. We find sufficient conditions under which these are also finitistic.