On topologization of transfinite convergence of sequences of real functions

Summary

Let κ be an infinite regular cardinal. We are concerned with the question when the κ-convergence is topologyzable. In particular, we show that if<span style='font-size:10.0pt;font-family:"Lucida Sans Unicode"'>cis regular then<span style='font-size:10.0pt; font-family:"Lucida Sans Unicode"'>c-convergence is topologyzable by the <<span style='font-size:10.0pt;font-family: "Lucida Sans Unicode"'>c-box topology on R ^R. Thus under CH the transfinite convergence is topologyzable. On the other hand, under MA+ØCH the transfinite convergence is not topologyzable.