# Local openness: Characterization of a robustness concept for generic sets in function spaces

*Mueller-Frank, Manuel*

*Journal of Mathematical Economics*, 2018, vol. 79, issue C, 173-178

**Abstract:**
This paper introduces a novel robustness concept for generic sets in function spaces. As motivation, I provide an economically relevant example of a functional property, where a subset of the domain with arbitrary small (Lebesgue) measure marks the difference between the functional property being strongly negligible (nowhere dense) or non-negligible (open). I define a functional property as locally open at some point of the domain if there exists a closed ball around the point such that the functional property is open in the continuous functions on the domain restricted to the ball. A functional property is open if and only if it is locally open everywhere on the domain. Further, a subset of the domain with arbitrary small measure marks the difference between an open and nowhere dense property if and only if the functional property is locally open almost everywhere on the domain.

**Keywords:** Generic set; Local openness; Residual set; Meager set; Constricting functions (search for similar items in EconPapers)

**Date:** 2018

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0304406817301192

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:79:y:2018:i:c:p:173-178

Access Statistics for this article

Journal of Mathematical Economics is currently edited by *Atsushi (A.) Kajii*

More articles in Journal of Mathematical Economics from Elsevier

Bibliographic data for series maintained by Dana Niculescu ().