Topology and its Applications最新文献

We provide the first explicit example of a cork of ${\mathrm{CP}}^2\#8\overline{{\mathrm{CP}}^2}$. This result gives the current smallest second Betti number of a standard simply-connected closed 4-manifold for which an explicit cork has been found.

We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [3], where it was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is $S^3$. In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin n-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce $S^3$ after Dehn surgery. Also, using a result of Birman and Menasco [4], we determine which closed pure 3-braids are hyperbolic.

Beben and Theriault proved a theorem on the homotopy fiber of an extension of a map with respect to a cone attachment, which has produced several applications. We give a short and elementary proof of this theorem.

Given a metric space X, we consider certain families of functions $f:X\to R$ having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When X is Polish, among them there are families of Baire measurable functions, $\bar{\mu }$-measurable functions (for a finite nonatomic Borel measure μ on X) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions.

In this article, we discuss some relationships of ω-balancedness and $(⁎)$ properties which were introduced for giving characterizations of subgroups of topological products of certain para(semi)topological groups. We mainly get the following results.

If G is a regular ω-balanced locally ω-good semitopological group with a q-point, then $Ir\left(G\right)\le \omega$ if and only if $Sm\left(G\right)\le \omega$. If G is a regular strongly paracompact semitopological group with a q-point and $Sm\left(G\right)\le \omega$, then G is completely ω-balanced if and only if G has property $\left({}^{⁎}\right)$. If G is a regular paracompact ω-balanced locally good semitopological group with a q-point and $Sm\left(G\right)\le \omega$, then G has property $(w⁎)$ if and only if G has property (**). If G is a regular metacompact semitopological group with a q-point and $Sm\left(G\right)\le \omega$, then G is MM-ω-balanced if and only if G is M-ω-balanced.

We show that a semitopological group G admits a homeomorphic embedding as a subgroup of a product of metrizable semitopological groups if and only if G is topologically isomorphic to a subgroup of a product of semitopological groups which are first-countable paracompact regular σ-spaces and is topologically isomorphic to a subgroup of a product of Moore semitopological groups.

An arrangement of pseudocircles $A$ is a collection of Jordan curves in the plane that pairwise intersect (transversally) at exactly two points. How many non-equivalent links have $A$ as their shadow? Motivated by this question, we study the number of non-equivalent positive oriented links that have an arrangement of pseudocircles as their shadow. We give sharp estimates on this number when $A$ is one of the three unavoidable arrangements of pseudocircles.

We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a question of Nyikos. One of the examples is a subspace of $(\omega +1)\times {\omega }_1$. In contrast, we show that every normal subspace of a finite power of ${\omega }_1$ is semi-proximal.

We say that an element x of a topological space X avoids measures if for every Borel measure μ on X if $\mu \left(\right\{x\left\}\right)=0$, then there is an open $U\ni x$ such that $\mu \left(U\right)=0$. The negation of this property can viewed as a local version of the property of supporting a strictly positive measure. We study points avoiding measures in the general setting as well as in the context of ${\omega }^{⁎}$, the remainder of Stone-Čech compactification of ω.

The objective of this work is to present some results related to some Erőds spaces. This paper answers a question made by the author in [12] proving that if X is a cohesive space then $K\left(X\right)$ is a cohesive space; we give a partial answer to question 7.3 of [7] providing an internal characterization of $Q\times E_c$-factors for certain subsets of $Q\times E_c$ and $E_c$; and we give conditions under which a perfect or open image of the complete Erdős space is homeomorphic to the complete Erdős space.

In this article, we consider the bipartite graphs $K_2\times K_n$. We prove that the connectedness of the complex $\text{Hom}(K_2\times K_n,K_m)$ is $m-n-1$ if $m\ge n$ and $m-3$ in all the other cases. Therefore, we show that for this class of graphs, $\text{Hom}(G,K_m)$ is exactly $(m-d-2)$-connected, $m\ge n$, where d is the maximal degree of the graph G.