José G. Anaya, Martha Hernández-Castañeda, David Maya
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引用次数: 0
摘要
符号 TD(X) 表示豪斯多夫空间 X 的所有非空完全断开紧凑子集的超空间。对于 Hausdorff 空间 f : X → Y 之间的映射，定义诱导映射 TD(f) ：TD(X)→TD(Y)定义为 TD(f)(A)=f(A)（f 下 A 的像）。在本文中，我们将研究 f 属于 Hausdorff 空间 𝕄 之间的一类映射的条件与 TD(f) 属于 𝕄 的条件之间的关系。
Induced mappings on the hyperspace of totally disconnected sets
The symbol TD(X) denotes the hyperspace of all nonempty totally disconnected compact subsets of a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y, define the induced mapping TD(f) : TD(X) → TD(Y) by TD(f)(A) = f(A) (the image of A under f). In the current paper, we study the relationships between the condition f belongs to a class of mappings between Hausdorff spaces 𝕄 and the condition TD(f) belongs to 𝕄.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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