标题： 线性序和实数轴 显示英文标题

标题： Linear Orders and the Real Line

摘要： 密集线性序（有/无端点）、可分线性序、完备线性序、线性序的可数链条件、Suslin线/Suslin树以及Suslin问题的定义。Cantor定理的陈述和证明，该定理将(Q,<)表征为在同构意义下唯一的可数密集线性序，没有端点，该推论将(R,<)表征为在同构意义下唯一的可分完备密集线性序，没有端点，每个可数线性序都可以嵌入到(Q,<)中（因此，嵌入到(R,<)中）。解释为什么Suslin线和Suslin树是等价的，什么是Aronszjan线/树，它是Suslin线/树的一个弱化形式。Suslin问题的历史和独立性。 显示英文摘要

摘要： Definitions of dense linear orders (with/without endpoints), separable linear orders, complete linear orders, the countable chain condition for linear orders, a Suslin line/Suslin tree and Suslin's problem Statement and proof of Cantor's Theorem characterizing (Q,<) as the only countable dense linear order without endpoints, up to isomorphism, the corollary which characterizes (R,<) as the only separable complete dense linear order without endpoints, every countable linear order embeds into (Q,<) (and thus, into (R,<)). Explanation of why Suslin lines and Suslin trees are equivalent, what an Aronszjan line/tree is, how it's a weakening of a Suslin line/tree. History and independence of Suslin's problem.