正则可分可数紧$\mathbb{R}$ -刚性空间
On regular separable countably compact $\mathbb{R}$-rigid spaces
摘要：
一个拓扑空间$X$称为{ \em $Y$ -rigid}，如果任何连续映射$f:X\rightarrow Y$是常数。在本文中，我们构造了一些正则可数紧$\mathbb R$ -刚性空间的例子，这些空间具有额外的性质，如可分性和第一可数性。这样我们就回答了Tzannes，Banakh，Ravsky的几个问题，并得到了$\mathbb R$ -刚性Nyikos空间的一个相容例子.证明了与ZFC一致的是，对每个基数$κ<\mathfrak c$，存在一个正则可分列紧空间$X$，它关于任何伪特征标为$\leqκ$的$T_1$空间$Y$是$Y$ -刚性的.
英文摘要：
A topological space $X$ is said to be {\em $Y$-rigid} if any continuous map $f:X\rightarrow Y$ is constant. In this paper we construct a number of examples of regular countably compact $\mathbb R$-rigid spaces with additional properties like separability and first countability. This way we answer several questions of Tzannes, Banakh, Ravsky, as well as get a consistent example of $\mathbb R$-rigid Nyikos space. Also, we show that it is consistent with ZFC that for every cardinal $κ<\mathfrak c$ there exists a regular separable countably compact space $X$ which is $Y$-rigid with respect to any $T_1$ space $Y$ of pseudocharacter $\leqκ$.
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