lcs空间(X,T)中的几个lcs拓扑

Some Locally Convex Separated Topologies in a lcs Space (X,T)

在ｌｃｓ空间（Ｘ，Ｔ）中证明了Ｔａａ（Ｔｋａ）是Ｘ上最大的与Ｔ有相同的绝对凸紧集（紧集）且与Ｔ相容的ｌｃｓ拓扑；（Ｔａ）０（（Ｔｋ）０）是Ｘ上最大的与Ｔ有相同的绝对凸紧集（紧集）且关于偶对（Ｘ，Ｘ′）容许的拓扑（ａｄｍｉｓｓｉｂｌｅｔｏｐｏｌｏｇｙ）．

In a lcs space (X,T), we prove that T aa (T ka ) is the largest lcs topology which has the same absolutely convex compact (compact) sets as T and is compatible with T;(T a) 0((T k) 0) is the largest lcs topology which has the same absolutely convex compact (compact) sets as T and is admissible with dual pair (X,X′). We also give an example for T aa (T a) 0.