论文标题
在某些较弱的Scheepers属性上
On certain weaker forms of the Scheepers property
论文作者
论文摘要
我们介绍了Scheepers属性的较弱形式，即几乎是Scheepers（$ {\ sf as} $），从Sakai（$ {\ sf ws} $）的意义上讲，Scheepers弱的Scheepers和Kočinac（$ {\ sf ws_k} $）的Scheepers和弱的Scheepers。我们探讨了Scheepers属性较弱形式的许多拓扑特性，并提供了几乎没有说明性的例子来区分这些空间。当所有较弱的形式均等时，考虑某些情况。我们还对本文有关基础性的弱变异进行了调查。特别是我们观察到 1。如果$ x $的每个有限功率是$ {\ sf am} $（分别为$ {\ sf wm} $），则$ x $ is $ {\ sf as} $（分别为$ {\ sf ws} $）。 2。基数的每个几乎每个小于$ \ mathfrak {d} $都是$ {\ sf as} $。 3。令$ x $是Lindelöf和$κ<\ Mathfrak d $。如果$ x $是$κ$多$ {\ sf ah} $的结合（分别为$ {\ sf wh} $，$ {\ sf wh_k} $ spaces，则$ x $ is $ {\ sf as} $（分别为} $（$ {\ sf ws} $，$ {\ sf ws} $，$，$，$，$，$ {\ sf ws__________________________ 4。$ x $的Alexandroff重复$ ad（x）$具有Scheepers属性，并且仅当$ ad（x）$才具有$ {\ sf ws_k} $属性。 5。如果$ ad（x）$是$ {\ sf as} $（分别为$ {\ sf ws} $），则$ x $也是$ {\ sf as} $（分别为$ {\ sf ws} $）。 此外，很少有关于$ {\ sf as} $的观察，有效地$ {\ sf ws} $，并且提出了有效的$ {\ sf ws_k} $空间。还给出了一些开放问题。
We introduce the weaker forms of the Scheepers property, namely almost Scheepers (${\sf aS}$), weakly Scheepers in the sense of Sakai (${\sf wS}$) and weakly Scheepers in the sense of Kočinac (${\sf wS_k}$). We explore many topological properties of the weaker forms of the Scheepers property and present few illustrative examples to make distinction between these spaces. Certain situations are considered when all the weaker forms are equivalent. We also make investigations on the weak variations as considered in this paper concerning cardinalities. In particular we observe that 1. If every finite power of a space $X$ is ${\sf aM}$ (respectively, ${\sf wM}$), then $X$ is ${\sf aS}$ (respectively, ${\sf wS}$). 2. Every almost Lindelöf space of cardinality less than $\mathfrak{d}$ is ${\sf aS}$. 3. Let $X$ be Lindelöf and $κ<\mathfrak d$. If $X$ is a union of $κ$ many ${\sf aH}$ (respectively, ${\sf wH}$, ${\sf wH_k}$) spaces, then $X$ is ${\sf aS}$ (respectively, ${\sf wS}$, ${\sf wS_k}$). 4. The Alexandroff duplicate $AD(X)$ of a space $X$ has the Scheepers property if and only if $AD(X)$ has the ${\sf wS_k}$ property. 5. If $AD(X)$ is ${\sf aS}$ (respectively, ${\sf wS}$), then $X$ is also ${\sf aS}$ (respectively, ${\sf wS}$). Besides, few observations on productively ${\sf aS}$, productively ${\sf wS}$ and productively ${\sf wS_k}$ spaces are presented. Some open problems are also given.
