@misc{10481/71429,
year = {2021},
month = {8},
url = {http://hdl.handle.net/10481/71429},
abstract = {Many authors consider that the main pillars of Functional Analysis are the Hahn–Banach
Theorem, the Uniform Boundedness Principle and the Open Mapping Principle. The first
one is derived from Zorn’s Lemma, while the latter two usually are obtained from Baire’s
Category Theorem. In this paper we show that these three pillars should be either just two
or at least eight, since the Uniform Boundedness Principle, the Open Mapping Principle and
another five theorems are equivalent, as we show in a very elemental way. Since one can
give an almost trivial proof of the Uniform Boundedness Principle that does not require the
Baire’s theorem, we conclude that this is also the case for the other equivalent theorems that,
in this way, are simultaneously proved in a simple, brief and concise way that sheds light on
their nature.},
organization = {Universidad de Granada/CBUA},
organization = {Junta de Andalucia	FQ199},
organization = {IMAG-Maria de Maeztu Grant	CEX2020-001105-M/AEI/10.13039/501100011033},
publisher = {Springer},
keywords = {Uniform boundedness},
keywords = {Open mapping},
keywords = {Closed graph},
keywords = {Banach isomorphism},
keywords = {Norms theorem},
keywords = {Sum theorem},
keywords = {Closed range},
title = {On the pillars of Functional Analysis},
doi = {10.1007/s13398-021-01108-1},
author = {Velasco Collado, María Victoria},
}