线性空间中的共逼近

Coapproximation in Linear Spaces

本文研究了在局部凸空间和赋范线性空间中的（f-）共逼近和强（f-）共逼近的一些性质,给出了f-共逼近、强f-共逼近和强f-Kolmogorov集的特征定理.并举例说明G.S.Rao[3]的两主要定理是不正确的,同时作了相应的更正.所得的结果中的部分推广和改进了Song[1,2]、Rao[3]和Narang[5]等人的相应结果.

In this paper,we study some properties of (f-) coapproximation and strongly (f-) coapproximation in locally convex spaces and normed linear spaces. The characterization theorems of (f-) coapproximation, strongly (f-) coapproximation, and strongly (f-) Kol-mogorov set in locally convex spaces are obtained. Meanwhile, we give two examples to show that two main theorems of G. S. Rao[3] do not hold, and then establish the corresponding correct results, parts of our results extend and improve the corresponding results due to Song[1,2]、Rao[3]、Narang[6] and other authors.