<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We give a proof of the uniform boundedness principle for linear continuous maps from <italic>F</italic> -spaces into topological vector spaces which is elementary and also quite simple.</p>
</abstract>

We give a proof of the uniform boundedness principle for linear continuous maps from F -spaces into topological vector spaces which is elementary and also quite simple.

A Really Simple Elementary Proof of the Uniform Boundedness Principle in <italic>F</italic> -Spaces

Department of Mathematics and Computer Sciences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Really Simple Elementary Proof of the Uniform Boundedness Principle in  -Spaces

We give a proof of the uniform boundedness principle for linear continuous maps from F -spaces into topological vector spaces which is elementary and also...

A Really Simple Elementary Proof of the Uniform Boundedness Principle in F -Spaces

Published Online: Jun 18, 2024

Page range: -

Received: Mar 28, 2024

Accepted: Jun 03, 2024

DOI: https://doi.org/10.2478/amsil-2024-0017

Keywords
uniform boundedness, Baire category, metric linear space, topological vector space

© 2024 José L. Ansorena, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Really Simple Elementary Proof of the Uniform Boundedness Principle in F -Spaces

Published Online: Jun 18, 2024

Page range: -

Received: Mar 28, 2024

Accepted: Jun 03, 2024

DOI: https://doi.org/10.2478/amsil-2024-0017

Keywordsuniform boundedness, Baire category, metric linear space, topological vector space

© 2024 José L. Ansorena, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
uniform boundedness, Baire category, metric linear space, topological vector space