Vol. 40, No. 1, 1972

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On removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy

Robin B. S. Brooks

Vol. 40 (1972), No. 1, 45–52
Abstract

It is known that if f,g : X Y are maps of a topological space X into a topological manifold Y , and that f and g can be deformed by homotopies to maps fand gf which are coincidence-free, then f may be deformed by a homotopy to a map f′′ such that f′′ and g are coincidence-free. This result is generalized as follows: If f,g : X Y are maps of a topological space X into a topological manifold Y and ff and gare homotopic to f and g respectively, then for any homotopy {gt} from g to g, there is a homotopy {ft} from ff such that the set of coincidences of ft and g1t is the same for all t [0,1]. Some applications of this result to fixed point theory and root theory are indicated.

Mathematical Subject Classification
Primary: 55C20
Milestones
Received: 27 July 1970
Published: 1 January 1972
Authors
Robin B. S. Brooks