A LOWER BOUND FOR THE DELTA-NIELSEN NUMBER

A LOWER BOUND FOR THE DELTA-NIELSEN NUMBER

This paper is concerned with the number of solutions of three kinds of equations. Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equations we will study are (1) f(x) = g(x), (2) f(x) = y sub 0, and (3) h(x) = x. In a previous paper, the first author de...

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Bibliographische Detailangaben
Hauptverfasser: Brooks,Robin B. S, Brown,Robert F
Format: Report
Sprache:eng
Schlagworte:
EQUATIONS
HAUSDORFF SPACE
MAPPING(TRANSFORMATIONS)
MATHEMATICS
Numerical Mathematics
THEOREMS
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Zusammenfassung:This paper is concerned with the number of solutions of three kinds of equations. Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equations we will study are (1) f(x) = g(x), (2) f(x) = y sub 0, and (3) h(x) = x. In a previous paper, the first author defined a lower bound N for the number of solutions of these equations which remains such a lower bound when f,g, and h are moved through homotopies. The number N is called the Delta-Nielsen number of the equation. Prepared in cooperation with California Univ., Los Angeles, under Grant NSF-GP-4018.