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

Mohsen Soltanifar

doi:10.20944/preprints202308.0904.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 10 August 2023 / Approved: 11 August 2023 / Online: 11 August 2023 (09:49:44 CEST)

In this paper, we classify the function space of all real-valued functions on R denoted as F(R,R) into 28 distinct blocks. 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 four well-known real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

real-valued functions; cardinals; Cantor function; Thomae function; Weierstrass function; Dirichlet function; partition

Computer Science and Mathematics, Analysis

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

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