Regular closed maps
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- by R. F. Dickman PDF
- Proc. Amer. Math. Soc. 39 (1973), 414-416 Request permission
Abstract:
A subset $A$ of $X$ is far from the remainder if whenever $\mathcal {U}$ is a free open ultrafilter in $X$ there exists $U \in \mathcal {U}$ such that $A \cap {\text {c}}{{\text {l}}_X}U = \emptyset$. 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.References
- A. Błaszczyk and J. Mioduszewski, On factorization of maps through $\tau X$, Colloq. Math. 23 (1971), 45–52. MR 305331, DOI 10.4064/cm-23-1-45-52
- R. F. Dickman Jr., On closed extensions of functions, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 326–332. MR 270344, DOI 10.1073/pnas.62.2.326
- Chen-tung Liu, Absolutely closed spaces, Trans. Amer. Math. Soc. 130 (1968), 86–104. MR 219024, DOI 10.1090/S0002-9947-1968-0219024-9
- Giovanni Viglino, Extensions of functions and spaces, Trans. Amer. Math. Soc. 179 (1973), 61–69. MR 322785, DOI 10.1090/S0002-9947-1973-0322785-3
Additional Information
- © Copyright 1973 American Mathematical Society
- 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