Formula omitted]-connected spaces and the images of metric spaces

Abstract

In this paper we discuss the following Tkachuk's question in the sense of ideal convergence [16,18]: Is any Tychonoff connected sequential space a quotient image of a connected metric space? It is proved that let I be an ideal on the set N then a topological space X is an I-connected space with an I-csf-network if and only if X is a continuous I-covering image of a connected metric space. It follows that a topological space X is a connected I-sequential space with an I-csf-network if and only if X is a quotient I-covering image of a connected metric space.