功率均匀的密封性和密封性的变化
Power homogeneous compacta and variations on tightness
摘要：
在[6]中引入的弱紧性$wt(X)$具有性质$wt(X)\leq t(X)$。文[4]证明了，若$X$是齐次紧集，则$|X|\leq 2^{wt(X)πχ(X)}$是齐次紧集.引入了几乎紧性$at(X)$，并证明了若$X$是幂齐次紧，则$|X|\leq 2^{at(X)πχ(X)}$是紧的.这改进了\arhangelskii，van Mill和Ridderbos在[2]中关于幂齐次紧$X$有$|X|\leq 2^{t(X)}$的结果，并部分回答了[4]中的一个问题.另外，当$X$是齐次Hausdorff空间时，我们证明了$|X|\leq 2^{pw_cL(X)wt(X)πχ(X)pct(X)}$，改进了[3]中的一个结果.它还将[4]中的结果推广到Hausdorff设置中。Bella和Spadaro在[5]中引入的基数不变量$pwL_c(X)$满足$pwL_c(X)\leq L(X)$和$pwL_c(X)\leq c(X)$。我们还显示了一个齐次空间$X$的重量$w(X)$是有界的在各种情况下使用$wt(X)$。一个这样的结果是，如果$X$是均匀和规则的，那么$w(X)\leq 2^{L(X)wt(X)pct(X)}$。这推广了文献[4]中的一个结果：若$X$是齐次紧集，则$w(X)\leq 2^{wt(X)}$.
英文摘要：
The weak tightness $wt(X)$, introduced in [6], has the property $wt(X)\leq t(X)$. It was shown in [4] that if $X$ is a homogeneous compactum then $|X|\leq 2^{wt(X)πχ(X)}$. We introduce the almost tightness $at(X)$ with the property $wt(X)\leq at(X)\leq t(X)$ and show that if $X$ is a power homogeneous compactum then $|X|\leq 2^{at(X)πχ(X)}$. This improves the result of \arhangelskii, van Mill, and Ridderbos in [2] that $|X|\leq 2^{t(X)}$ for a power homogeneous compactum $X$ and gives a partial answer to a question in [4]. In addition, if $X$ is a homogeneous Hausdorff space we show that $|X|\leq 2^{pw_cL(X)wt(X)πχ(X)pct(X)}$, improving a result in [3]. It also extends the result in [4] into the Hausdorff setting. The cardinal invariant $pwL_c(X)$, introduced in [5] by Bella and Spadaro, satisfies $pwL_c(X)\leq L(X)$ and $pwL_c(X)\leq c(X)$. We also show the weight $w(X)$ of a homogeneous space $X$ is bounded in various contexts using $wt(X)$. One such result is that if $X$ is homogeneous and regular then $w(X)\leq 2^{L(X)wt(X)pct(X)}$. This generalizes a result in [4] that if $X$ is a homogeneous compactum then $w(X)\leq 2^{wt(X)}$.
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