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Abstract

Let $c$ be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_\infty (A, c)$ the set of all bounded continuous functions $f:A\to c$, and $C_A(X, c)$ the set of all functions $f:X\to c$ which are continuous at each point of $A \subset X$. We show that a Tikhonov subspace $A$ of a topological space $X$ is strong Choquet in $X$ if there exists a monotone extender $u: C_\infty (A, c)\to C_A(X, c)$. This shows that the monotone extension property for bounded $c$-valued functions can fail in GO-spaces, which provides a negative answer to a question posed by I. Banakh, T. Banakh and K. Yamazaki.