description/proof of that for
Topics
About:
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
- 3: Proof
Starting Context
-
The reader knows a definition of
vectors bundle. - The reader knows a definition of section along subset of codomain of continuous surjection.
- The reader knows a definition of closed set.
- The reader knows a definition of neighborhood of subset.
- The reader knows a definition of support of map from topological space into field.
-
The reader admits the proposition that for any
vectors bundle and any section from any subset of the base space at any point where , there is a extension on an open-neighborhood-of-point domain. -
The reader admits the proposition that for any map between any arbitrary subsets of any
manifolds with boundary at any point, where includes , the restriction on any domain that contains the point is at the point. -
The reader admits the proposition that for any open cover of any
manifold, there is a partition of unity subordinate to the cover. - The reader admits the proposition that for any locally finite set of subsets of any topological space, the closure of the union of the subsets is the union of the closures of the subsets.
Target Context
-
The reader will have a description and a proof of the proposition that for any
vectors bundle, any section along any closed subset of the base space can be extended to over the whole base space with the support contained in any open neighborhood of the subset.
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:
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Statements:
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2: Natural Language Description
For any
3: Proof
Whole Strategy: Step 1: for each point,
Step 1:
For each point,
Step 2:
Step 3:
Let us define
Step 4:
Let us define
Step 5:
For each point,