作为稠密连通图的不可分连通度量空间

Connected economically metrizable spaces

A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a nonseparably connected complete metric space Eco(X) under a monotone quotient map. The metric d of the space Eco(X) is economical in the sense that for each infinite subspace A of X the cardinality of the set {d(a,b):a,b in A} does not exceed the density of A. The construction of the space Eco(X) determines a functor Eco from the category Top of topological spaces and their continuous maps into…

Widely-connected sets in the bucket-handle continuum

A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a completely metrizable example that answers a question of Paul Erdős and Howard Cook, while a similar example answers a question of Jerzy Mioduszewski.

Simply Connected 3-Manifolds with a Dense Set of Ends of Specified Genus

We show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\{e_i\}$ so that, for every $i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in $S^3$. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.

稠密伪紧与稠密连通空间的刻画

The characterizations of dense-pseudocompact and dense-connected spaces

本文定义了稠密拓扑性质，并分别给出了Tychonoff空间下稠密伪紧、稠密连通以及稠密超连通空间的等价刻画，同时推广至拓扑群等结构。

连通F-空间

A connected F-space

我们给出了一个例子，一个紧凑的连接F-空间与连续的实值函数f，其内部的纤维的工会是不稠密的。这间接地回答了阿布拉莫维奇和基托弗的一个否定的问题。

紧连通群弧分支中的超序列

Super-sequences in the arc component of a compact connected group

设G是交换拓扑群.符号\hat{G}表示具有紧开拓扑的所有连续特征标χ：G --> T的群。如果x（E）\subseteq ≠（[-1/4，1/4]）仅对平凡特征标χ \in \hat{G}成立，则称G的子集E在G中是qc-稠密的，其中x：R --> T = R/Z是标准同态.一个超序列是一个非空的紧致T2空间S，其中至多有一个非孤立点（S收敛到该点）。证明了无限紧阿贝尔群G是连通的当且仅当它的弧分支G_a包含一个收敛到0的超序列且在G中是qc-稠密的.这给出了Aussenhofer最近的一个定理：对于连通的局部紧阿贝尔群G，由r（χ）= χ \restriction_{G_a}定义的限制同态r：\hat{G} --> \hat{G}_a，对于χ \in \hat{G}，是拓扑同构。我们还证明了一个无限紧群G是连通的当且仅当它的弧分支G_a包含一个超序列S，S收敛于生成G的一个稠密子群的恒等式e（等价地，S \setminus {e}是G在Hofmann和Morris意义下的一个无限适集）.