Some Properties And Characterizations Of Nearly Weak Submetacompact Spaces

The thesis is composed of three chapters. First, it gives a comprehensivedefinition of nearly weak submetacompact spaces. Then the following research isbased on the properties it has. Nearly weak submetacompact spaces is the promotionof weak submetacompact spaces,Its research has important signification to CoverProperties.This kind of research on nearly spaces, can date back to1969, whenM.K.Singal and other persons quoted the concept of nearly paracompact spaces firstly.It set off a surge of topology.After that, many scholars did lots of research on this kindof space, referring to their different or similar properties. In this thesis, it will give acomprehensive definition of nearly weak submetacompact space. And the two mainparts of its properties well analyzed in the thesis are the closed hereditary andTychonoff product properties,and the relationship with the compact spaces. Referringto Tychonoff product, it can be divided into threeparts:limited countably, unlimitedcountably, unlimited uncountably products. And the key point of thisthesis is aboutthe Tychonoff products on the nearly weak submetacompact spaces,Get equivalentcharacterizations of unlimited elements and other equivalent theorems.