Kumar, Vinod; Kamboj, Devender Kumar On hyperconnected topological spaces. (English) Zbl 1389.54041 An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 62, No. 2, Part 1, 275-283 (2016). Summary: It is proved that there is only one open ultrafilter iff the space is hyperconnected. Relations of functions demi-open, skeletal and o-ultra, obtained without and with regard to hyperconnectedness, are used to prove that the full subcategory HypTop of Top, consisting of all hyperconnected spaces, is a subcategory of the category skelTOP of all topological spaces with morphisms skeletal continuous functions. HypTop is proved to be mono-epireflective in skelTop by showing that there exists a functor from skelTOP to HypTop turning skelTop into the largest subcategory of Top where the functor is a reflection. Also, skelTop is found to be a maximal subcategory of TOP such that HypTop is reflective in the subcategory with reflection morphisms skeletal functions. MSC: 54B30 Categorical methods in general topology 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54G05 Extremally disconnected spaces, \(F\)-spaces, etc. Keywords:hyperconnected space; o-ultrafilter; skeletal function; o-ultra function PDFBibTeX XMLCite \textit{V. Kumar} and \textit{D. K. Kamboj}, An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 62, No. 2, Part 1, 275--283 (2016; Zbl 1389.54041)