<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We present a Helly type theorem for sequences of functions with values in metric spaces and apply it to representations of some mappings on the space of continuous functions. A generalization of the Riesz theorem is formulated and proved. More concretely, a representation of certain majored linear operators on the space of continuous functions into a complete metric space.</p></abstract>

We present a Helly type theorem for sequences of functions with values in metric spaces and apply it to representations of some mappings on the space of continuous functions. A generalization of the Riesz theorem is formulated and proved. More concretely, a representation of certain majored linear operators on the space of continuous functions into a complete metric space.

A Helly theorem for functions with values in metric spaces

Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814-73 Bratislava SLOVAKIA

Faculty of Natural Sciences University of Matej Bel Tajovského 40 SK–974-01 Banská Bystrica SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"A Helly theorem for functions with values in metric spaces"}

We present a Helly type theorem for sequences of functions with values in metric spaces and apply it to representations of some mappings on the space of...

A Helly theorem for functions with values in metric spaces

Published Online: Nov 12, 2012

Page range: 159 - 168

DOI: https://doi.org/10.2478/v10127-009-0056-z

Keywords
metric space, vector space, vector function, bounded variation, majored operator

This content is open access.

A Helly theorem for functions with values in metric spaces

Published Online: Nov 12, 2012

Page range: 159 - 168

DOI: https://doi.org/10.2478/v10127-009-0056-z

Keywordsmetric space, vector space, vector function, bounded variation, majored operator

This content is open access.

Keywords
metric space, vector space, vector function, bounded variation, majored operator