论文标题
在$κ$ -PSEUDOCOCTACTESS和功能空间的均匀同态性上
On $κ$-pseudocompactess and uniform homeomorphisms of function spaces
论文作者
论文摘要
如果每个连续的映射$ f $ $ x $ $ x $ in $ \ mathbb {r}^κ$ the Image $ f（x）$是紧凑的，则tychonoff space $ x $称为$κ$ -PSEUDOCOMPACT。该概念概括了假发性，并给出了位于假发和紧凑空间之间的空间的分层。众所周知，$ x $的伪混合度是由功能空间的均匀结构$ c_p（x）$连续实现函数的$ x $上的$ x $所赋予的点置。关于A.V. Arhangel'skii在[Topology Appl。，89（1998）]中问，如果$κ$ -PseudoCompactnesments类似主张是正确的。我们为这个问题提供了肯定的答案。
A Tychonoff space $X$ is called $κ$-pseudocompact if for every continuous mapping $f$ of $X$ into $\mathbb{R}^κ$ the image $f(X)$ is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying between pseudocompact and compact spaces. It is well known that pseudocompactness of $X$ is determined by the uniform structure of the function space $C_p(X)$ of continuous real-valued functions on $X$ endowed with the pointwise topology. In respect of that A.V. Arhangel'skii asked in [Topology Appl., 89 (1998)] if analogous assertion is true for $κ$-pseudocompactness. We provide an affirmative answer to this question.
