Corresponding to [27], some properties of S-closed subspaces and subsets -closed relative to a topological space are proved. Conditions under which mappings preserve certain -closed subspaces are investigated.
Relativamente al [27], sono provate alcune proprieta dei sottoinsiemi -chiusi di uno spazio topologico. Sono studiate delle condizioni mediante le quali le applicazioni conservano alcuni sottospazi -chiusi.
@article{BUMI_2007_8_10B_2_469_0,
author = {Zbigniew Duszy\'nski},
title = {Remarks on $\mathcal{S}$-Closedness in Topological Spaces},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {10-A},
year = {2007},
pages = {469-483},
zbl = {1139.54002},
mrnumber = {2339455},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_469_0}
}
Duszyński, Zbigniew. Remarks on $\mathcal{S}$-Closedness in Topological Spaces. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 469-483. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_469_0/
[1] - - , β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77-90. | MR 828081
[2] , Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32. | MR 854426 | Zbl 0604.54002
[3] , On some mappings in topological spaces, Bull. Cal. Math. Soc., 61 (1969), 127-135. | MR 281167 | Zbl 0215.51605
[4] , Properties of S-closed spaces, Proc. Amer. Math. Soc., 72 (1978), 581-586. | MR 514999 | Zbl 0408.54018
[5] , Some maximal topologies which are QHC, Proc. Amer. Math. Soc., 75 (1979), 149-156. | MR 529232 | Zbl 0417.54002
[6] , Locally nearly compact spaces, Boll. Un. Mat. Ital., 6 (4) (1972), 146-153; | MR 321013 | Zbl 0257.54020
[7] - , Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci., 22 (1971), 123-126.
[8] - , Semi-topological properties, Fundamenta Mathematicae, 74 (1972), 233-254. | MR 301690 | Zbl 0206.51501
[9] , , On s-closed spaces, Indian J. Pure Appl. Math., 18 (3) (1987), 226-233. | MR 880176 | Zbl 0625.54031
[10] - - , On the topology generated by semi-regular sets, Indian J. Pure Appl. Math., 25 (11) (1994), 1163-1170. | MR 1303248 | Zbl 0851.54025
[11] - , Contra-semicontinuous functions, Math. Pannon., 10 (2) (1999), 159-168. | MR 1704605 | Zbl 0932.54014
[12] , Topology, Allyn and Bacon, Inc., Boston1966. | MR 193606
[13] , On pre-semi-open mappings, submitted. | MR 2548306 | Zbl 1201.54018
[14] , On some classes of subsets in extremally disconnected spaces, to appear in Far East J. Mat. Sci. (2007). | MR 2797812
[15] , On some concepts of weak connectedness of topological spaces, Acta Math. Hungar., 110 (1-2) (2006), 81-90. | MR 2198416
[16] , , Somewhat continuous functions, Czechoslovak Mathematical Journal, 21(96) (1971), 5-12. | MR 278269 | Zbl 0222.54010
[17] , Almost continuous mappings, Prace Mat., 10 (1966), 1-7. | MR 220256 | Zbl 0138.17601
[18] , A note on mappings of extremally disconnected spaces, Acta Math. Hungar., 46 (1-2) (1985), 83-92. | MR 819058 | Zbl 0597.54037
[19] , Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41. | MR 166752 | Zbl 0113.16304
[20] - - , On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53. | MR 830896 | Zbl 0571.54011
[21] - - , α-continuous and α-open mappings, Acta Math. Hungar., 41 (1983), 213-218. | MR 703734
[22] , On certain generalizations of the notion of continuity, Mat. Casopis, 23 (4) (1973), 374-380. | MR 339051
[23] , On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970. | MR 195040 | Zbl 0137.41903
[24] , On semi-continuous mappings, Lincei-Rend. Sc. fis. mat. e nat., 54 (1973), 210-214. | MR 350686
[25] , On semi-spaces, Ann. Soc. Sci. Bruxelles, 90 (1976), 215-220. | MR 405348
[26] , On S-closed spaces, Ann. Soc. Sci. Bruxelles, 91 (1977), 189-194. | MR 474204 | Zbl 0408.54017
[27] , On S-closed subspaces, Lincei-Rend. Sc. fis. mat. e nat., 64 (1978), 157-162. | MR 551642
[28] , Semi-continuity and weak-continuity, Czechoslovak Mathematical Journal, 31(106) (1981), 314-321. | MR 611084 | Zbl 0483.54006
[29] , A function which preserves connected spaces, Cas. pest. mat., 107 (1982), 393-396. | MR 683820 | Zbl 0511.54008
[30] , On a-continuous functions, Cas. pest. mat., 109 (1984), 118-126. | MR 744869 | Zbl 0544.54009
[31] , On semi-homeomorphisms, Boll. Un. Mat. Ital., (5) 16-A (1979), 501-509. | MR 551374 | Zbl 0424.54002
[32] - , Spazi semiconnessi a spazi semiaperti, Rend. Circ. Mat. Palermo, 24 (2) (1975), 273-285. | MR 464149
[33] - , Connectedness and strong semi-continuity, Čas. pěst. mat., 109 (1984), 261-265. C | MR 755590 | Zbl 0553.54005
[34] , Weak openness and almost openness, Internat. J. Math. and Math. Sci., 7(1) (1984), 35-40. | MR 743822 | Zbl 0562.54020
[35] , Weak continuity and almost continuity, Internat. J. Math. and Math. Sci., 7(2) (1984), 311-318. | MR 757276 | Zbl 0552.54007
[36] - , Almost-continuous mappings, Yokohama Math. J., 16 (1968), 63-73. | MR 261569 | Zbl 0191.20802
[37] , I-compact subsets, Boll. Un. Mat. Ital., (6) 3-B (1984), 87-98. | MR 744431
[38] , Weakly Hausdorff spaces and cardinality of topological spaces, General Topology and its application to Modern Analysis and Algebra III, Proc. Conf. Kanpur 1968, Academia, Prague, (1977), 301-306. | MR 283746
[39] , , On regular semi-open sets and s*-closed spaces, Tamkang J. Math., 23(4) (1992), 337-348. | MR 1204644 | Zbl 0780.54020
[40] , S-closed spaces, Proc. Amer. Math. Soc., 60 (1976), 335-338. | MR 425899
[41] , Topics in functional analysis, Lecture Notes in Mathematics, vol. 45, Springer-Verlag1967. | MR 223854 | Zbl 0156.36103