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I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ...

I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...

I need some help in order to formulate a proof of Proposition 11.3.5 - 4 ...

Garling's statement and proof of Proposition 11.3.5 reads as follows:

View attachment 8964Can someone please help me formulate a formal and rigorous proof that \(\displaystyle A \subseteq A^{ \bot \bot }\) ... ... ?Help will be much appreciated ...

Peter

I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...

I need some help in order to formulate a proof of Proposition 11.3.5 - 4 ...

Garling's statement and proof of Proposition 11.3.5 reads as follows:

View attachment 8964Can someone please help me formulate a formal and rigorous proof that \(\displaystyle A \subseteq A^{ \bot \bot }\) ... ... ?Help will be much appreciated ...

Peter