A Classification of Elements of Function Space F(<mml:semantics>R</mml:semantics>,<mml:semantics>R</mml:semantics>)

被引:0
|
作者
Soltanifar, Mohsen [1 ,2 ,3 ]
机构
[1] Northeastern Univ, Coll Profess Studies, Analyt Div, 1400-410 West Georgia St, Vancouver, BC V6B 1Z3, Canada
[2] Univ Toronto, Dalla Lana Sch Publ Hlth, Biostat Div, 620-155 Coll St, Toronto, ON M5T 3M7, Canada
[3] ClinChoice Inc, Biostat & Programming Div, Biometr Dept, 750-2 Robert Speck Pkwy, Mississauga, ON L4Z 1H8, Canada
关键词
real-valued functions; cardinals; Cantor function; Thomae function; Weierstrass function; Dirichlet function; partition;
D O I
10.3390/math11173715
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
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页数:10
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