General Topology - Finite Product Topology

Harry Huang (aka Wenyuan Huang, 黄问远)
  2024-11-19 23:00 2024-11-19 23:00 Created   2024-11-27 18:02:58 2024-11-27 18:02:58 Updated      

I hate topology. --- By Woziji Shuode

RECAP

Please read to "General Topology - Topology and Basis" first.

The Product Topology on

Definition 1. [Product Topology]

Let and be topological spaces, then is a basis of $X Y, while is open in and is open in .

Definition 2. [Projection]

Theorem 3.

If is a basis of and is a basis of , then is a basis for the topology of .

Theorem 4.

is a subbasis for the product topology on .

  • Title: General Topology - Finite Product Topology
  • Author: Harry Huang (aka Wenyuan Huang, 黄问远)
  • Created at : 2024-11-19 23:00:00
  • Updated at : 2024-11-27 18:02:58
  • Link: https://whuang369.com/blog/2024/11/19/Math/Topology/General_Topology_Finite_Product_Topology/
  • License: This work is licensed under CC BY-NC-SA 4.0.
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General Topology - Finite Product Topology
  1. 1. RECAP
  2. 2. The Product Topology on