Abstract: Based on the convergence of directed sets,the concepts of strongly continuous top ological spaces and strong topology are introduced.It is proved that all strongly continuous spaces are continuous spaces,and counter-examples are provided to demonstrate that continuous spaces are not necessarily strongly continuous spaces.Furthermore,the insertion property of approximation relations on strongly continuous spaces is explained,and the conditions for the equivalence between strongly continuous spaces and approximation spaces are established.

Key words: directed spaces, continuous spaces, strong topology, strong continuous spaces