On regular-invariance of continuity

Abstract:

Let $(X,\sigma )$ be a given topological space. A compression $\tau$ of $\sigma$ is regular-invariant if and only if for every regular space $Y$ the $\sigma$-continuous functions into $Y$ are also $\tau$-continuous. $\sigma$ is regular minimal if no proper compression of $\sigma$ is regular-invariant. J. A. Guthrie and H. E. Stone posed the problem of whether every semiregular space is regular minimal. We answer this question in the negative.