Hahn-Banach 2nd Geometric Form(FASSPDE)

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Theorem 1.4 Hahn-Banach 2nd Geometric Form

Result

This makes it possible for us to use a closed hyperplane to strictly separate a closed convex subset and a compact convex subset where no common areas of them could be found.

Remark

Proof(See Appendix Above)

The proof of Theorem 1.4 is by setting C = A – B and three claims (1)C is closed (2)C is convex (3)0 does not live inside C, then apply the properties of open balls and the result of Theorem 1.3

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

Related Topics

Corollary 1.4.1

Statement

Result

This gives us a possible choice in proving that F is dense in E, since it suffices to prove that everywhere continuous linear functional on E that vanishes on F must vanish everywhere on E.

Remark

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

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