Abstract:Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, $\wp$, and present properties of it.
Keywords: additivity; almost connected im kleinen; analytic set; aposyndetic continuum; atomic map; continuum; decomposable continuum; $G_\delta$ set; hyperspace; indecomposable continuum; monotone map; property of Kelley; set function $\mathcal{K}$; set function $\mathcal{T}$; set function $\wp$; set functions continuous on continua; uniform property of Effros; upper semicontinuous function
DOI: DOI 10.14712/1213-7243.2025.002
AMS Subject Classification: 54B20 54C60 54F16