A Lower Bound for the Delta-Nielson Number.

Robin B. S. Brooks, Robert Goodell Brown

Expert InsightsPublished 1967

This Paper is concerned with the number of solutions of three kinds of equations: Let f and g be maps of a space X into a space H, and let H be a map of X into itself, and let y be in Y. The equations studied are: f(x)=g(x); f(x)=y; and h(x)=x. In his doctoral dissertation, Brooks 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. It is not, in general, possible to compute this number for particular spaces and maps directly from its definition. This Paper defines a positive integer J, which is easier to compute than N and which has the property that J is less than or equal to N. 19 pp. Refs.

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  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1967
  • Document Number: P-3634

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Brooks, Robin B. S. and Robert Goodell Brown, A Lower Bound for the Delta-Nielson Number. Santa Monica, CA: RAND Corporation, 1967. https://www.rand.org/pubs/papers/P3634.html.
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