arXiv math/06080352006-08-01math.GNmath.LO

First Countable Continua and Proper Forcing

Joan E. Hart, Kenneth Kunen

英文摘要：

Assuming the Continuum Hypothesis, there is a compact first countable connected space of weight aleph_1 with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add reals.

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

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

Remarks on countable tightness

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelof property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are…

2013-10-20math.GNmath.LO

Compact Scattered Spaces in Forcing Extensions

We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models where the continuum is aleph_2 in which no such space can have aleph_2 countable levels.

2004-08-03math.GNmath.LO

两个非平凡可数维连续统的乘积不能轻映射到任何因子中

No product of two non-trivial countable-dimensional continua maps lightly into any of the factors

本文证明了正维数紧可度量化空间的乘积在特定连续映射下，其因子必包含无一维子集的非平凡连续统，从而对 J. Dudák 和 B. Vejnar 的问题给出了否定回答。

2025-03-18math.GN

Submaximal spaces and cardinal invariants

We give a combinatorial characterization of countable submaximal subspaces of $2^κ$. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of $2^{ω_1}$ whilst $\mathfrak{c}=ω_2$. Combining this with previous results, we construct a disjointly tight countable irresolvable space of weight $<\mathfrak{c}$, answering a question of Bella and Hrušák.

2021-12-07math.GNmath.LO

强适当力迫对拓扑性质的保持

Preservation of Topological Properties by Strongly Proper Forcings

本文证明强适当力迫保持拓扑空间的可数紧致度、Lindelöf、Rothberger、Menger 及 Rothberger 策略版本等性质，推广了 Dow、Iwasa 和 Kada 的结果。

2024-10-02math.GNmath.LO

弧状连续统平面嵌入中可数集的可接近性

Accessibility of countable sets in plane embeddings of arc-like continua

本文研究弧状连续统的平面嵌入问题，证明了在特定条件下逆向极限存在使给定可数集所有点均可接近的嵌入，并应用于 Knaster 连续统及构造了作为平面同胚吸引子的新嵌入。

2024-07-23math.DSmath.GN

更多相关论文收起更多论文

$\mathsf{PFA}$ and $ω_1$-free compact spaces

The Proper Forcing Axiom implies that compact Hausdorff spaces are either first-countable or contain a converging $ω_1$-sequence.

2021-11-11math.GNmath.LO

Wilder continua and their subfamilies as coanalytic absorbers

The family of Wilder continua in cubes of dimension > 2 and its two subfamilies-of continuum-wise Wilder continua and of hereditarily arcwise connected continua-are recognized as coanalytic absorbers in the hyperspace of subcontinua of the cubes. In particular, each of them is homeomorphic to the set of all nonempty countable closed subsets of the unit interval.

2016-04-05math.GNmath.GT

Compact Spaces with a $P$-base

In the paper, we investigate (scattered) compact spaces with a $P$-base for some poset $P$. More specifically, we prove that, under the assumption $ω_1<\mathfrak{b}$, any compact space with an $ω^ω$-base is first-countable and any scattered compact space with an $ω^ω$-base is countable. These give positive solutions to Problems 8.6.9 and 8.7.7 in \cite{Banakh2019}. Using forcing, we also prove that in a model of $ω_1<\mathfrak{b}$, there is a non-first-countable compact space with a $P$-base for some poset $P$ with calibre~$ω_1$.

2021-05-24math.GN

SPM Bulletin 12

In this issue we celebrate the appearance of the proceedings of the first SPM Workshop, announce several mathematical breakthroughs, have two extended contributions by Babinkostova, and a new open problem by Kalenda. Contents: Editor's note; Proceedings of the first workshop on Coverings, Selections, and Games in Topology; A five element basis for the uncountable linear orders; Set mapping reflection; The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis; A solution to the L space problem and related ZFC constructions; Countable Tightness, Elementary Submodels and Hom…

2005-07-05math.COmath.GNmath.LO

Continuum Without Non-Block Points

For any composant $E \subset \mathbb H^*$ and corresponding near-coherence class $\mathscr E \subset ω^*$ we prove the following are equivalent : (1) $E$ properly contains a dense semicontinuum. (2) Each countable subset of $E$ is contained in a dense proper semicontinuum of $E$. (3) Each countable subset of $E$ is disjoint from some dense proper semicontinuum of $E$. (4) $\mathscr E $ has a minimal element in the finite-to-one monotone order of ultrafilters. (5) $\mathscr E $ has a $Q$-point. A consequence is that NCF is equivalent to $\mathbb H^*$ containing no proper dense semicontinuum and…

2020-07-17math.GN

On the cardinality of separable pseudoradial spaces

The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question here is if there is, in ZFC, a regular (or just Hausdorff) SP of cardinality greater than $\mathfrak c$. While this question is left open, we establish a number of non-trivial results that we list: 1. It is consistent with Martin's Axiom and $\mathfrak c =\aleph_2$ that there is a countably tight and compact SP of cardinality $2^{\mathfrak c}$. 2. If $κ$ is a measurable cardinal then in the forcing extension obtained by…

2020-12-08math.GN