definition of Euclidean topological space
Topics
About: topological space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
- 3: Note
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of Euclidean topology.
Target Context
- The reader will have a definition of Euclidean topological space.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\(*\mathbb{R}^n\): with the Euclidean topology
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Conditions:
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2: Natural Language Description
Any \(\mathbb{R}^n\) together with its Euclidean topology
3: Note
It is important to be clear on these: \(\mathbb{R}^n\) is just a set without any topology, which means that there is no proximity between points to say nothing of distance; Euclidean topological space does not imply any metric by itself, although many people say just "Euclidean" meaning having the Euclidean metric.
