论文标题
强烈可计数（半）Hausdorff空间的示例
Examples of strongly rigid countable (semi)Hausdorff spaces
论文作者
论文摘要
如果每个非恒定连续地图$ f：x \ to x $是$ x $的身份映射，则拓扑空间$ x $是$ $ $ jirst $。 Hausdorff拓扑空间$ X $称为$ BROWN $，如果任何非空缺套件$ u，v \ subseteq x $交叉点$ \ bar u \ cap \ cap \ bar v $是无限的。我们证明，每个可容纳$τ'$的每个可容纳的棕色Hausdorff Space $ X $都可以使$ x'=（x，τ'）$是一个非常僵硬的抗抗乳状棕色空间。此结构得出了一个可数可数的抗药性Hausdorff Space $ x $的一个示例，这是一个强烈的严格性，这是在数学上提出的两个问题，这是对数学上的两个问题。通过相同的方法，我们构造了一个强刚性的$ k_2 $ - 可将其含有非关闭的紧凑型子集的半高效应空间，该空间回答了Mathoverflow上其他两个问题。
A topological space $X$ is $strongly$ $rigid$ if each non-constant continuous map $f:X\to X$ is the identity map of $X$. A Hausdorff topological space $X$ is called $Brown$ if for any nonempty open sets $U,V\subseteq X$ the intersection $\bar U\cap\bar V$ is infinite. We prove that every second-countable Brown Hausdorff space $X$ admits a stronger topology $τ'$ such that $X'=(X,τ')$ is a strongly rigid anticompact Brown space.This construction yields an example of a countable anticompact Hausdorff space $X$ which is strongly rigid, which answers two problems posed at MathOverflow. By the same method we construct a strongly rigid $k_2$-metrizable semi-Hausdorff space containing a non-closed compact subset, which answers two other problem posed at MathOverflow.
