It is well known that the property of being a bounded set in the class of topological vector spaces E is not a topological property, where a subset \(B\subset E\) is called a bounded set if every neighbourhood of zero U in E absorbs B. The paper deals with the problem which topological properties of bounded sets for the space \(C_{k}(X)\) (of continuous real-valued functions on a Tychonoff space X with the compact-open topology) endowed with the weak topology of \(C_{k}(X)\) can be transferred to bounded sets of \(C_{k}(Y)\) endowed with the weak topology, assuming that the corresponding weak topologies of both \(C_{k}(X)\) and \(C_{k}(Y)\) are homeomorphic.

它公知的是的是在类拓扑向量空间的有界集的属性Ë不是拓扑性质，其中的一个子集\（B \子集ë\）被称为有界集合如果零的每附近ü在ë吸收乙。本文讨论的问题是，空间\（C_ {k}（X）\）的有界集的拓扑性质（具有紧实开放拓扑的Tychonoff空间X上的连续实值函数）具有弱拓扑的\（C_ {K}（X）\）可以被转移到有界集合的\（C_ {K}（Y）\）假设\（C_ {k}（X）\）和\（C_ {k}（Y）\）的相应弱拓扑都是同胚的。