Localizations in universal topological categories

Localizations in universal topological categories
HTML articles powered by AMS MathViewer

by F. Cagliari and S. Mantovani PDF

Proc. Amer. Math. Soc. 103 (1988), 639-640 Request permission

For some familiar topological categories it is shown that the subcategory of indiscrete spaces is the only nontrivial localization.

References

Francesca Cagliari and Sandra Mantovani, On disconnectednesses in subcategories of a topological category and related topics, Rend. Circ. Mat. Palermo (2) Suppl. 12 (1986), 205–212. Second topology conference (Taormina, 1984). MR 853160
C. Cassidy, M. Hébert, and G. M. Kelly, Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. Ser. A 38 (1985), no. 3, 287–329. MR 779198
Horst Herrlich and George E. Strecker, Category theory, 2nd ed., Sigma Series in Pure Mathematics, vol. 1, Heldermann Verlag, Berlin, 1979. An introduction. MR 571016
Th. Marny, On epireflective subcategories of topological categories, General Topology Appl. 10 (1979), no. 2, 175–181. MR 527843, DOI 10.1016/0016-660x(79)90006-0
G. Preuss, Relative connectednesses and disconnectednesses in topological categories, Quaestiones Math. 2 (1977/78), no. 1-3, 297–306. MR 500841
Claus Michael Ringel, Monofunctors as reflectors, Trans. Amer. Math. Soc. 161 (1971), 293–306. MR 292907, DOI 10.1090/S0002-9947-1971-0292907-X