Mathematics – General Topology
Scientific paper
2009-01-02
Fund. Math. 212 (2011), 145-173
Mathematics
General Topology
20 pages
Scientific paper
A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a nonseparably connected complete metric space Eco(X) under a monotone quotient map. The metric d of the space Eco(X) is economical in the sense that for each infinite subspace A of X the cardinality of the set {d(a,b):a,b in A} does not exceed the density of A. The construction of the space Eco(X) determines a functor Eco from the category Top of topological spaces and their continuous maps into the category Metr of metric spaces and their non-expanding maps.
Banakh Taras
Vovk M.
Wójcik Michal Ryszard
No associations
LandOfFree
Connected economically metrizable spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Connected economically metrizable spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connected economically metrizable spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380866