Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hahn-Banach Theorem: a proof of the equivalence between the analitic
  and geometric versions   We present here a simple and direct proof of the classic geometric version of
Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal
implication, and the direct proofs of both versions, are already well kown, but
they are also summarized. For the complex case, in both versions the
Hahn-Banach Theorem is deduced from the real case, as it is well known.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat