Characterize core-compactness of the continuous-random-variable space

Determine whether $\mathcal{CV}^\surd_1X$ is core-compact whenever the underlying $T_0$ space $X$ is core-compact.

Background

The paper identifies further topological questions concerning the space CV1√X\mathcal{CV}^\surd_1X of normalized √\surd-max continuous random variables. Core-compactness is particularly relevant because core-compact spaces form a Cartesian closed category, which is important for developing semantics for monads. The paper leaves unresolved whether this property is inherited from XX by the associated random-variable space.

References

And we are also interested in more topological properties on $\mathcal{CV}\surd_1$, such as whether $\mathcal{CV}\surd_1X$ is core-compact when $X$ is.

— Monad Structures on Topological Spaces Comprising Mislove's Random Variables  (2608.18683 - Zhou et al., 19 Aug 2026) in Section Conclusion and future work