首页/论文/1311.2011

arXiv 1311.20112013-11-29math.GN

C_k（X）型的可积可数紧空间

Productively countably tight spaces of the form C_k(X)

Leandro Fiorini Aurichi, Renan Maneli Mezabarba

备注：: Notation for the compact-open topology changed; Theorem 3.5 improved

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

摘要英文摘要相关论文

摘要：

利用代数学得到了C_k理论中的一些结果。研究了具有紧开拓扑的连续实函数空间在什么条件下是可积可数紧空间，给出了Alster空间的一些应用.

英文摘要：

Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology is a productively countably tight space, which yields some applications on Alster spaces.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

拓扑对策与乘积可数紧空间

Topological games and productively countably tight spaces

这个工作的两个主要结果如下：如果空间$X$是这样的，即参与人II在游戏中对每个$x \in X$都有获胜策略$\gone(Ω_x, Ω_x)$，那么$X$是生产可数紧的.另一方面，如果一个空间是生产可数紧的，那么$\sone(Ω_x, Ω_x)$对每个$x \in X$都成立。有了这些结果，其他几个结果如下，使用的一些特征所作的Uspenskii和Scheepers。

2014-04-06math.GN

Indestructibly productively Lindelöf and Menger function spaces

For a Tychonoff space $X$ and a family $λ$ of subsets of $X$, we denote by $C_λ(X)$ the $T_1$-space of all real-valued continuous functions on $X$ with the $λ$ -open topology. A topological space is productively Lindelöf if its product with every Lindelöf space is Lindelöf. A space is indestructibly productively Lindelöf if it is productively Lindelöf in any extension by countably closed forcing. In this paper, we study indestructibly productively Lindelöf and Menger function space $C_λ(X)$.

2018-10-10math.GN

乘积Lindelof空间与不可结构Lindelof空间

Productively Lindelof and Indestructibly Lindelof Spaces

最近有相当大的兴趣在生产林德洛夫空间，即空间，使他们的产品与每个林德洛夫空间是林德洛夫。在这里，我们对这种空间做一些相关的评论。不可破坏的林德洛夫空间，即在每一个可数闭力迫扩张中保持林德洛夫的空间，由Tall在1995年引入。Scheepers和Tall在2010年探索了它们与拓扑博弈和选择原则的联系。我们在这里找到了更多的联系。

2012-10-30math.GNmath.LO

Productively Lindelöf spaces of countable tightness

Michael asked whether every productively Lindelöf space is powerfully Lindelöf. Building of work of Alster and De la Vega, assuming the Continuum Hypothesis, we show that every productively Lindelöf space of countable tightness is powerfully Lindelöf. This strengthens a result of Tall and Tsaban. The same methods also yield new proofs of results of Arkhangel'skii and Buzyakova. Furthermore, assuming the Continuum Hypothesis, we show that a productively Lindelöf space $X$ is powerfully Lindelöf if every open cover of $X^ω$ admits a point-continuum refinement consisting of basic open sets. This …

2017-11-21math.GNmath.LO

On $σ$-countably tight spaces

Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $σ$-countably tight compactum has cardinality $\mathfrak{c}$ remains open. We also show that if an arbitrary product is $σ$-countably tight then all but finitely many of its factors must be countably tight.

2016-07-02math.GN

可数紧致性在$\sigma$-紧致空间中不是离散自反的

Countable tightness is not discretely reflexive in $σ$-compact spaces

本文构造了多个$\sigma$-紧致空间（部分在ZFC中，部分在附加公理下），它们本身不满足可数紧致性，但所有离散子集的闭包却满足可数紧致性，甚至第一可数，从而否定了可数紧致性的离散自反性。

2024-11-07math.GN

更多相关论文收起更多论文

关于可数紧性的注记

Remarks on countable tightness

可数紧性可以被可数闭强迫所破坏。我们的特点是不可摧毁的可数紧密性下可数封闭强迫的组合语句类似的高用来表征不可摧毁的林德洛夫财产下可数封闭强迫。我们考虑可数紧性的一般扩张通过添加科恩实数的行为。我们证明了某些类的拓扑空间是不可破坏可数紧的。更强版本的可数紧密性，包括选择性版本的可分性，进一步探讨。

2013-10-20math.GNmath.LO

在可数紧与$ω$ -有界之间

Between countably compact and $ω$-bounded

给定$T_1$空间$X$的子空间的一个性质$P$，我们称$X$是{ \em $P$ -bounded}当且仅当$X$的每个具有性质$P$的子空间在$X$中有紧闭包.在这里，我们研究$P$有界空间的性质$P \in \{ωD, ωN, C_2 \}$，其中$ωD \, \equiv$“可数离散”，$ωN \, \equiv$“可数无处密集”，和$C_2 \,\equiv$“第二可数”。显然，对于这些$P$ -有界的每一个都是在可数紧和$ω$ -有界之间。我们在ZFC中给出了分离所有这些有界性属性及其适当组合的例子。同时给出了具有更好性质（如：更小的基数或权、局部紧性、第一可数性）的一致分离实例。关于$ωD$ -有界空间，我们有一些有趣的结果，表明$ωD$ -有界性比可数紧性强得多：$\bullet$ Lindelöf度为$< cov(\mathcal{M})$的正则$ωD$ -有界空间是$ω$ -有界的。具有可数紧度的正则$\bullet$-有界空间是$ωN$ -有界的，如果$\mathfrak{b} > ω_1$则甚至是$ω$ -有界的. $\bullet$如果Hausdorff空间的乘积是$ωD$ -有界的，那么它的因子除了一个之外都是$ω$ -有界的.至多$\bullet$许多Hausdorff $ωD$ -有界空间的乘积是可数紧的.作为一个副产品，我们得到的规则，可数紧，可数…

2014-06-30math.GN

A note on the tightness of $G_δ$-modifications

We construct a normal countably tight $T_1$ space $X$ with $t(X_δ) >2^ω$. This is an answer to the question posed by Dow-Juhász-Soukup-Szentmiklóssy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_δ$-modifications of countably tight spaces can be arbitrary large up to the least $ω_1$-strongly compact cardinal.

2019-07-15math.GNmath.LO

具有不可分测度的可数紧对偶球

Countably tight dual ball with a nonseparable measure

本文在钻石原理假设下构造了一个紧空间K，使得P(K)可数紧但K上存在不可数Maharam型的Radon测度，从而区分了P(K×K)与P(K)×P(K)的紧性并回答了Pol的问题。

2023-12-05math.FAmath.GNmath.LO

$G_δ$ covers of compact spaces

We solve a long standing question due to Arhangel'skii by constructing a compact space which has a $G_δ$ cover with no continuum-sized ($G_δ$)-dense subcollection. We also prove that in a countably compact weakly Lindelöf normal space of countable tightness, every $G_δ$ cover has a $\mathfrak{c}$-sized subcollection with a $G_δ$-dense union and that in a Lindelöf space with a base of multiplicity continuum, every $G_δ$ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Vega's celebrated theorem on th…

2017-07-16math.GN

PFA（S）[S]与局部紧正规空间

PFA(S)[S] and Locally Compact Normal Spaces

本文研究了PFA（S）[S]型模型中的局部紧正规空间，特别刻画了仿紧的可数紧空间，即不包含Ω_1的完美原像且所有可分闭子空间都是Lindelof的空间.

2011-04-18math.GNmath.LO

A note on $δ$-strongly compact cardinals

In this paper we investigate more characterizations and applications of $δ$-strongly compact cardinals. We show that, for a cardinal $κ$ the following are equivalent: (1) $κ$ is $δ$-strongly compact, (2) For every regular $λ\ge κ$ there is a $δ$-complete uniform ultrafilter over $λ$, and (3) Every product space of $δ$-Lindelöf spaces is $κ$-Lindelöf. We also prove that in the Cohen forcing extension, the least $ω_1$-strongly compact cardinal is a precise upper bound on the tightness of the products of two countably tight spaces.

2020-09-24math.GNmath.LO

非林德洛夫空间中的最终常数和停滞函数

Eventually Constant and stagnating functions in non-Lindelöf spaces

研究非林德洛夫空间中函数性质，引入推广林德洛夫性的四个性质$\mathsf{P}(X,Y)$，研究其与其他拓扑性质关系，给出如特定树子空间、流形等相关结果示例，部分结果是对前人工作的重新表述。

2026-07-23math.GN