In this paper, it is shown that a mapping from a sequential space is continuous iff it is sequentially continuous, which improves a result by relaxing first-countability of domains to sequentiality. An example is also given to show that open mappings do not imply Darboux-mappings, which answers a question posed by Wang and Yang.

Author Bio

Xun Ge is from Suzhou, P. R. China. He is a student at Depatment of Mathematics, Suzhou University and is interested in mathematics. He explored the topic of continuous mappings during the Sping 2005 and began this paper at that time. He is looking forward to receiving advice and comments relating to his research.