论文标题
不可逆转的同喻和不可逆的Lusternik-Schnirelmann类别的概念
Irreversible homotopy and a notion of irreversible Lusternik-Schnirelmann category
论文作者
论文摘要
这项工作旨在研究不可逆过程和自然现象的模型。为此，我们介绍了不可逆转的路径的概念（对于简洁的道路，我们编写了IR-Path），IR-HOMOTOPY，IR合同空间和Lusternik-Schnirlann IR类别，通过将$ i = [0,1] $配备和左订单拓扑。我们将定义的不可逆性限制为$ t_0 $的空间，以便对于$ t_1 $的空格，IR-PATHS是恒定的。在提供了这些概念的一些定理和属性之后，我们最终证明了Lusternik-Schnirmann IR类别是IR-HOMOTOPY等效性的不变性。
This work was intended as an attempt to investigate a model of irreversible process and natural phenomena. For this, we introduce the notion of irreversible path (that for brevity we write ir-path), ir-homotopy, ir-contractible space, and Lusternik-Schnirelmann ir-category by equipping the $I=[0,1]$ with left order topology. We will restrict the irreversibility of definitions to $T_0$ Spaces, such that for $T_1$ spaces, the ir-paths are constant. After providing some theorems and properties of these notions, eventually, we prove that Lusternik-Schnirelmann ir-category is an invariant of ir-homotopy equivalence.
