Regular closed maps
Author:
R. F. Dickman
Journal:
Proc. Amer. Math. Soc. 39 (1973), 414-416
MSC:
Primary 54C10
DOI:
https://doi.org/10.1090/S0002-9939-1973-0315654-1
MathSciNet review:
0315654
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Abstract | References | Similar Articles | Additional Information
Abstract: A subset of
is far from the remainder if whenever
is a free open ultrafilter in
there exists
such that
. A map is regular closed provided that the image of every regular closed set is closed. In this note we use some recent results of G. Viglino to show that every map can be extended to a regular closed map with far from the remainder point inverses. We also relate these maps to several other interesting classes of maps.
- [1]
A. Blaszczyk and J. Mioduszewski, On factorization of maps through
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- [2] R. F. Dickman, Jr., On closed extensions of functions, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 326-332. MR 42 #5233. MR 0270344 (42:5233)
- [3] C. T. Liu, Absolutely closed spaces, Trans. Amer. Math. Soc. 130 (1968), 86-104. MR 0219024 (36:2107)
- [4] G. Viglino, Extensions of functions and spaces, Trans. Amer. Math. Soc. (to appear). MR 0322785 (48:1146)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0315654-1
Keywords:
Regular closed maps,
absolutely closed maps
Article copyright:
© Copyright 1973
American Mathematical Society