Strong insertion of a $\gamma-$ continuous function
DOI:
https://doi.org/10.5269/bspm.v34i2.19642Palavras-chave:
Strong insertion, Strong binary relation, Preopen set, Semi-open set, $\gamma-$open set, Lower cut setResumo
Necessary and sufficient conditions in terms of lower cut sets are given for the strong insertion of a $\gamma-$continuous function between two comparable real-valued functions.In this paper, is given a sufficient condition for the weak $\gamma-$insertion property. Also for a space with the weak $\gamma-$insertion property, we give necessary and sufficient conditions for the space to have the strong $\gamma-$insertion property. Several insertion theorems are obtained as corollaries of these results.Referências
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2. H. Blumberg, New properties of all functions, Trans. Amer. Math. soc. 24 (1922) 113-128.
3. F. Brooks, Indefinite cut sets for real functions, Amer. Math. Monthly 78 (1971) 1007-1010.
4. H. H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math. 8 (1964) 351-360.
5. J. Dontchev, The characterization of some peculiar topological space via - and -sets, Acta Math. Hungar. 69 (1-2) (1995) 67-71.
6. M. Ganster and I. Reilly, A decomposition of continuity, Acta Math. Hungar. 56 (3-4) (1990) 299-301.
7. T. Husain, Almost continuous mappings, Prace Mat. 10 (1966) 1-7.
8. M. Katetov, On real-valued functions in topological spaces, Fund. Math. 38 (1951) 85-91.
9. M. Katetov, Correction to, "On real-valued functions in topological spaces", Fund. Math. 40 (1953) 203-205.
10. E. Lane, Insertion of a continuous function, Pacific J. Math. 66 (1976) 181-190.
11. N. Levine, Semi-open sets and semi-continuity in topological space, Amer. Math. Monthly 70 (1963) 36-41.
12. A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982) 47-53.
13. M. Mirmiran, Insertion of a function belonging to a certain subclass of RX, Bull. Iran. Math. Soc. Vol. 28, No. 2 (2002) 19-27.
14. M. Mirmiran, Insertion of a
-continuous function, Bull. Iran. Math. Soc.Vol. 37, No. 3 (2011) 171-181.
15. M. Przemski, A decomposition of continuity and -continuity, Acta Math. Hungar. 61 (1-2) (1993) 93-98.
16. V. Ptak, On complete topological linear spaces, Czech. Math. J. 78 (1953) 301-360.
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2015-06-01
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