关于凸子集和(绝对)收缩核

ON CONVEX SETS AND (ABSOLUTE) RETRACTS

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核,以及在什么情况下为绝对收缩核。

In this paper we discuss relations among approximative neighborhood retracts, absolute neighborhood retracts and neighborhood retracts in the linear metric spaces. Especially, we obtain the following results: (1). If A is a closed convex subset in a linear metric space L, A is a neighborhood retract of L iff A is a approximative neighborhood retract of L; (2). If absolute neighborhood retract A is a subset of a space X , A is a approximative neighborhood retract of X; (3). If X is a convex subset of a linear metric space, and absolute neighborhood retract A is a dense convex subset of X, X is a absolute retract iff for any open set U containing A, X\U is a Z-set of X.