2023/12/19 by Juhász, István, van Mill, Jan
#54A25 #54C30 #54D05 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2312.12257
If X is a topological space and Y is any set then we call a family F of maps from X to Y nowhere constant if for every non-empty open set U in X there is f ∈ F with |f[U]| > 1, i.e. f is not constant on U. We prove the following result that improves several earlier results in the literature. If X is a topological space for which C(X), the family of all continuous maps of X to ℝ, is nowhere constant and X has a π-base consisting of connected sets then X is \mathfrakc-resolvable.