A Classification of Elements of Function Space F ( R, R )

Mohsen Soltanifar ()
Additional contact information
Mohsen Soltanifar: Analytics Division, College of Professional Studies, Northeastern University, 1400-410 West Georgia Street, Vancouver, BC V6B 1Z3, Canada

Mathematics, 2023, vol. 11, issue 17, 1-10

Abstract: In this paper, we present a constructive description of the function space of all real-valued functions on R ( F ( R , R ) ) by presenting a partition of it into 28 distinct blocks and a closed-form formula for the representative function of each of them. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection , which reveals a special relationship structure between the well-known representatives of four of the blocks: the Cantor function, the Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

Keywords: real-valued functions; cardinals; Cantor function; Thomae function; Weierstrass function; Dirichlet function; partition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/17/3715/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/17/3715/ (text/html)

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:gam:jmathe:v:11:y:2023:i:17:p:3715-:d:1228021

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().