| This paper is presented as three sections. In the first section it is proved that Weierstrass's approximation theorem in read analysis is hold in function spaces endowed with set-open topology. In the second section we mainly discusses Ascoli theorem and prove that if there is some compact k-network under finite unions in function spaces Ascoli theorem is hold in set-open topology too. In the three section we show that a space has a point-countable weak base if and only if it is a 1-sequence-quotient, quotient and s-image of a metric space. Particularly, we prove that K-spaces are preserved by 1-sequence-quotient, closed mappings which answers a problem posed by Gu Jiansheng. |
