论文标题
关于同构组和开放式拓扑
On homeomorphism groups and the set-open topology
论文作者
论文摘要
在本文中，我们着重于拓扑空间$ x $的所有自塑形的组$ \ mathcal {h}（x）$上的固定拓扑，这些拓扑$ x $都产生了组操作，产品和逆功能的连续性。结果，我们使Dijkstra定理的更为笼统。在这种情况下，一个同质包围的家族$ \ MATHCAL {B} $由常规开放套件组成，并且从$ \ Mathcal {B} $中关闭每组的封闭均包含在有限的连接集合中，从$ \ Mathcal {B} $中包含。我们还证明，$ \ Mathcal {h}（x）$的零二氯拓扑是与$ \ Mathcal {h}的$ \ Mathcal {h}（x）$的$ \ Mathcal {h}（h h}（βx）$的$ x $ x $ $ x $ xere $ xereiention $ censeiention $ censeigtion $ censeiention $ censiention $ xere的相关性，均为$ can $ canseiention。相对于封闭子组的拓扑组。
In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we make the more general case of Dijkstra's theorem. In this case a homogeneously encircling family $\mathcal{B}$ consists of regular open sets and the closure of every set from $\mathcal{B}$ is contained in the finite union of connected sets from $\mathcal{B}$. Also we proved that the zero-cozero topology of $\mathcal{H}(X)$ is the relativisation to $\mathcal{H}(X)$ of the compact-open topology of $\mathcal{H}(βX)$ for any Tychonoff space $X$ and every homogeneous zero-dimensional space $X$ can be represented as the quotient space of a topological group with respect to a closed subgroup.
