Irreducible mapping

A continuous mapping of a topological space onto a topological space such that the image of every closed set in , other than itself, is different from . If is a continuous mapping, , and if all inverse images of points under are compact, then there exists a closed subspace in such that and such that the restriction of to is an irreducible mapping. The combination of the requirements on a mapping of being irreducible and being closed has an outstanding effect: Spaces linked by such mappings do not differ in a number of important characteristics; in particular, they have the same Suslin number and -weight. But the main value of closed irreducible mappings lies in the central role they play in the theory of absolutes.

References

[1]	A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)

Comments

See Absolute.

References

[a1]	J.R. Porter, R.G. Woods, "Extensions and absolutes of Hausdorff spaces" , Springer (1988)