SUBSTRONG CONVERGENCE OF THE FUNCTION SEQUENCE ON THE TOPOLOGICAI SPACE
Bai Renlun Department of Natural Science
DOI:10.11835/j.issn.1674-4764.1991.02.007
Received ,Revised , Accepted , Available online July 01, 2015
Volume ,1991,Pages -
- Abstract
The limit of convergent continuous function sequencemay be discontinuous.This makes difficults both in theory and applica-tion.For example,it makes the condition for operation of limits of integralof the function sequence become very strong.In general,it requiresuniform convergence to the function sequence.Therefore it is very imp-ortant to study such convergence as the limit of continuous function sequence,the limit is continuous.This paper studies a known substrong converg-ence of a function sequence in topological space and proves the necessaryand sufficient conditionof this convergence.