闭内射系统及其基本极限空间
Closed injective systems and its fundamental limit spaces
摘要：
本文对拓扑空间的所谓闭注入系统引入极限空间和基本极限空间的概念。给出了极限空间存在唯一性的主要结果和几个具体例子。在正文的主要部分，我们表明，封闭内射系统可以被认为是一个范畴的对象，其态射是所谓的顺式态射。此外，到基本极限空间的过渡可以被认为是从这个范畴到拓扑空间拓扑空间范畴的函子。随后，我们给出了归纳闭内射系统和基本极限空间的函子和反函子的性质。最后给出了一些特殊系统的基本极限空间的刻划结果，并研究了所谓的完美性质。
英文摘要：
In this article we introduce the concept of limit space and fundamental limit space for the so-called closed injected systems of topological spaces. We present the main results on existence and uniqueness of limit spaces and several concrete examples. In the main section of the text, we show that the closed injective system can be considered as objects of a category whose morphisms are the so-called cis-morphisms. Moreover, the transition to fundamental limit space can be considered a functor from this category into category of topological spaces. Later, we show results about properties on functors and counter-functors for inductive closed injective system and fundamental limit spaces. We finish with the presentation of some results of characterization of fundamental limite space for some special systems and the study of so-called perfect properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
