Abstract: The paper gives a sufficient and necessary condition for a weakly-weakly first-countable space to be a weakly first-countable space.It is proved that for a weakly-quasi first-countable space X, X is weakly first-countable if and only if X has the sequential point-G_δproperty and no closed copies of S_ω.We also prove that every weakly first-countable space(weakly-quasi first-countable space) is a quotient,two-to-one(countable-to-one) image of some first-countable space.As an application,a partial answer to a question posed by Lin Shou(2007) is obtained.
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: article
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot