General Topology - Order Topology

Harry Huang (aka Wenyuan Huang, 黄问远)

The Order Topology

Definition 8. [Order Topology]

Let be an ordered set. Then, is the collection of the following subsets:

  1. , with and ;
  2. , where and is the smallest element of ;
  3. , where and is the largest element of .

generates a topology , which is called Order Topology.

Definition 9. [Rays]

Let be a set with simple order relation, and . Then, the following kinds of subsets are called rays determined by :

  1. , also called open rays;
  2. , also called open rays;
  3. , also called closed rays;
  4. , also called closed rays;
  • Title: General Topology - Order Topology
  • Author: Harry Huang (aka Wenyuan Huang, 黄问远)
  • Created at : 2024-11-19 23:00:00
  • Updated at : 2024-11-27 18:03:13
  • Link: https://whuang369.com/blog/2024/11/19/Math/Topology/General_Topology_Order_Topology/
  • License: This work is licensed under CC BY-NC-SA 4.0.
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