Research On Quality Of Some Generalized Metric Spaces

People begin to research the product properties between 1940s and 1950s.From 1980s to 1990s,for researching the product properties of generalized paracompact spaces is developing. Some international prominent topologists,such as Y.Yajima (Japan) , G.Gruenhage(America), K.Chiba(Japan) and so on,have some important results to research the Tychonoff finite product properties, the Tychonoff countable infinite product properties, inverse limits, σ -products in generalized paracompact spaces.However,at present,the research results in the Tychonoff infinite uncountable product properties, inverse limits, Σ-products of generalized paracompact spaces are short.This paper use the mapping and covering methods to preliminary research the Tychonoff infinite uncountable producties , inverse linites,Σ -products of ortho compact space and hereditarily normal weak ((δθ)|—)-refinable space,and has mainly gained six results,three of that respectively extend and enrich the correlative conclusions of Doc. Teng Hui, Peiyong Zhu, and Nobuyuki KEMOTO.