Abstract
The aim of this paper is to answer the following question raised by J. Cobb and W. Voxman in 1980: If X is a connected space with a dispersion point p, and if ƒ: X→ X is a nonconstant continuous function, then is ƒ( p)= p? The answer to this question is negative, and we give a counterexample along with three theorems on a space with a dispersion point.
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