The separation theorem for quasi-closed sets
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- by John H. V. Hunt and Adalberto García-Máynez PDF
- Proc. Amer. Math. Soc. 27 (1971), 399-404 Request permission
Abstract:
The concepts of “closed set, separation and $n$-cell” are generalized to “quasi-closed set, weak separation and locally cohesive space,” respectively. It is then proved that any quasiclosed set $L$, which weakly separates two closed subsets $A,B$ in a locally cohesive ${T_1}$-space $X$, contains a closed set $K$ which separates $A - K$ and $B - K$ in $X$.References
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A. García-Máynez, Ph.D. Thesis, University of Virginia, Charlottesville, Va., 1968.
- Gordon T. Whyburn, Loosely closed sets and partially continuous functions, Michigan Math. J. 14 (1967), 193–205. MR 208578
- Gordon T. Whyburn, Quasi-closed sets and fixed points, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 201–205. MR 210111, DOI 10.1073/pnas.57.2.201 G. T. Whyburn, assisted by J. H. V. Hunt, Notes on functions and multifunctions, University of Virginia, Charlottesville, Va., 1966/67 (mimeographed notes).
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 399-404
- MSC: Primary 54.55
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276930-2
- MathSciNet review: 0276930