论文标题
在$ \ Mathcal {i} $ - 覆盖度量空间的图像
On $\mathcal{I}$-covering images of metric spaces
论文作者
论文摘要
令$ \ mathcal {i} $是$ \ mathbb {n} $的理想选择。映射$ f：x \ to y $称为$ \ mathcal {i} $ - 覆盖映射提供了一个序列$ \ {y_ {y_ {n} \} _ {n \ in \ mathbb n} $ is $ \ nathbb n} $ $ \ {x_ {n} \} _ {n \ in \ mathbb n} $收敛到$ x $ in $ x $中的point $ x $，因此$ x \ in f^{ - 1}（y）$ in f^{ - x_n $ in f^{-1}（y_n）$。在本文中，我们研究了具有某些$ \ MATHCAL {i} $ - $ CS $ -NETWORKS的空间，并研究了在某些$ \ Mathcal {i} $下的度量空间图像的表征，并覆盖映射，这会提示我们发现$ \ Mathcal {i} $ - $ CSF $ -Networks。获得以下主要结果： （1）一个$ x $具有$ \ mathcal {i} $ - $ csf $ -network，并且仅当$ x $是连续的，而$ \ natercal {i} $ - 覆盖度量空间的图像。 （2）空间$ x $是$ \ MATHCAL {i} $ - $ CSF $ - 可容纳空间，并且仅当$ x $是连续的$ \ Mathcal {i} $ - 覆盖和边界$ s $ s $ imimage a的公制空间。 （3）一个空格$ x $具有可点数的$ \ MATHCAL {i} $ - $ CS $ -NETWORD，并且仅当$ x $是连续的$ \ Mathcal {i} $ - 覆盖率 - 覆盖率 - $ s $ s $ - $ s $ - $ s $ imimage。
Let $\mathcal{I}$ be an ideal on $\mathbb{N}$. A mapping $f:X\to Y$ is called an $\mathcal{I}$-covering mapping provided a sequence $\{y_{n}\}_{n\in\mathbb N}$ is $\mathcal{I}$-converging to a point $y$ in $Y$, there is a sequence $\{x_{n}\}_{n\in\mathbb N}$ converging to a point $x$ in $X$ such that $x\in f^{-1}(y)$ and each $x_n\in f^{-1}(y_n)$. In this paper we study the spaces with certain $\mathcal{I}$-$cs$-networks and investigate the characterization of the images of metric spaces under certain $\mathcal{I}$-covering mappings, which prompts us to discover $\mathcal{I}$-$csf$-networks. The following main results are obtained: (1) A space $X$ has an $\mathcal{I}$-$csf$-network if and only if $X$ is a continuous and $\mathcal{I}$-covering image of a metric space. (2) A space $X$ is an $\mathcal{I}$-$csf$-countable space if and only if $X$ is a continuous $\mathcal{I}$-covering and boundary $s$-image of a metric space. (3) A space $X$ has a point-countable $\mathcal{I}$-$cs$-network if and only if $X$ is a continuous $\mathcal{I}$-covering and $s$-image of a metric space.
