线性空间中的共逼近

Coapproximation in Linear Spaces

中文关键词:  局部凸空间  强f-Kolmogorov集  （强）f-共逼近  赋范线性空间

英文关键词:locally convex spaces  strongly （f-） Kolmogorov set  （strongly）（f-） coapproxi-mation  normed linear spaces.

中文摘要:

      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、Rao和Narang等人的相应结果.

英文摘要:

      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 do not hold, and then establish the corresponding correct results, parts of our results extend and improve the corresponding results due to Song、Rao、Narang and other authors.