论文标题
研究某些类别的功能及其与$ s $ embeddedness的联系
Studies of certain classes of functions and its connection with $S$-embeddedness
论文作者
论文摘要
如果$ f $在每个硬式子集中（一种特殊的封闭子集）上，我们将$ c（x）$中的函数$ f $称为$ x $。如果每种$ t $的连续功能可以连续扩展到$ x $，我们将$ x $的子集$ t $ $ x $归为$ s $。每个$ s $ - 安排的子集为$ c^*$ - 嵌入。在本文中，我们给出了相反部分的特征。为了获得相反，我们遇到了一种函数，该功能在子集的每个硬子集中都远离零。我们进一步研究了这种类型的功能以及硬结合功能的属性。
We call a function $f$ in $C(X)$ to be hard-bounded if $f$ is bounded on every hard subset, a special kind of closed subset, of $X$. We call a subset $T$ of $X$ to be $S$-embedded if every hard-bounded continuous function of $T$ can be continuously extended upto $X$. Every $S$-embedded subset is $C^*$-embedded. In this paper we have given a characterization of the converse part. To get the converse, we came across a type of function which are bounded away from zero on every hard subset of a subset. We further studied few properties of this type of functions and also of hard-bounded functions.
