Remarks on 𝒮 -Closedness in Topological Spaces

Zbigniew Duszyński

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 469-483
  • ISSN: 0392-4033

Abstract

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Corresponding to [27], some properties of S-closed subspaces and subsets 𝒮 -closed relative to a topological space are proved. Conditions under which mappings preserve certain 𝒮 -closed subspaces are investigated.

How to cite

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Duszyński, Zbigniew. "Remarks on $\mathcal{S}$-Closedness in Topological Spaces." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 469-483. <http://eudml.org/doc/290415>.

@article{Duszyński2007,
abstract = {Corresponding to [27], some properties of S-closed subspaces and subsets $\mathcal\{S\}$-closed relative to a topological space are proved. Conditions under which mappings preserve certain $\mathcal\{S\}$-closed subspaces are investigated.},
author = {Duszyński, Zbigniew},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {469-483},
publisher = {Unione Matematica Italiana},
title = {Remarks on $\mathcal\{S\}$-Closedness in Topological Spaces},
url = {http://eudml.org/doc/290415},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Duszyński, Zbigniew
TI - Remarks on $\mathcal{S}$-Closedness in Topological Spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 469
EP - 483
AB - Corresponding to [27], some properties of S-closed subspaces and subsets $\mathcal{S}$-closed relative to a topological space are proved. Conditions under which mappings preserve certain $\mathcal{S}$-closed subspaces are investigated.
LA - eng
UR - http://eudml.org/doc/290415
ER -

References

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  1. ABD EL-MONSEF, M. E. - EL-DEEB, S. N. - MAHMOUD, R. A., β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77-90. MR828081
  2. ANDRIJEVIC, D., Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32. Zbl0604.54002MR854426
  3. BISWAS, N., On some mappings in topological spaces, Bull. Cal. Math. Soc., 61 (1969), 127-135. Zbl0215.51605MR281167
  4. CAMERON, D. E., Properties of S-closed spaces, Proc. Amer. Math. Soc., 72 (1978), 581-586. Zbl0408.54018MR514999DOI10.2307/2042476
  5. CAMERON, D. E., Some maximal topologies which are QHC, Proc. Amer. Math. Soc., 75 (1979), 149-156. Zbl0417.54002MR529232DOI10.2307/2042691
  6. CARNAHAN, D. A., Locally nearly compact spaces, Boll. Un. Mat. Ital., 6 (4) (1972), 146-153; Zbl0257.54020MR321013
  7. CROSSLEY, C. G. - HILDEBRAND, S. K., Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci., 22 (1971), 123-126. 
  8. CROSSLEY, C. G. - HILDEBRAND, S. K., Semi-topological properties, Fundamenta Mathematicae, 74 (1972), 233-254. Zbl0206.51501MR301690DOI10.4064/fm-74-3-233-254
  9. DI MAIO, G., NOIRI, T., On s-closed spaces, Indian J. Pure Appl. Math., 18 (3) (1987), 226-233. Zbl0625.54031MR880176
  10. DLASKA, K. - ERGUN, N. - GANSTER, M., On the topology generated by semi-regular sets, Indian J. Pure Appl. Math., 25 (11) (1994), 1163-1170. Zbl0851.54025MR1303248
  11. DONTCHEV, J. - NOIRI, T., Contra-semicontinuous functions, Math. Pannon., 10 (2) (1999), 159-168. Zbl0932.54014MR1704605
  12. DUGUNDJI, J., Topology, Allyn and Bacon, Inc., Boston1966. MR193606
  13. DUSZYNSKI, Z., On pre-semi-open mappings, submitted. Zbl1201.54018MR2548306
  14. DUSZYNSKI, Z., On some classes of subsets in extremally disconnected spaces, to appear in Far East J. Mat. Sci. (2007). MR2797812
  15. DUSZYNSKI, Z., On some concepts of weak connectedness of topological spaces, Acta Math. Hungar., 110 (1-2) (2006), 81-90. MR2198416DOI10.1007/s10474-006-0008-x
  16. GENTRY, K. R., HOYLE III, H. B., Somewhat continuous functions, Czechoslovak Mathematical Journal, 21(96) (1971), 5-12. Zbl0222.54010MR278269
  17. HUSAIN, T., Almost continuous mappings, Prace Mat., 10 (1966), 1-7. Zbl0138.17601MR220256
  18. JANKOVIC, D. S., A note on mappings of extremally disconnected spaces, Acta Math. Hungar., 46 (1-2) (1985), 83-92. Zbl0597.54037MR819058DOI10.1007/BF01961010
  19. LEVINE, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41. Zbl0113.16304MR166752DOI10.2307/2312781
  20. MASHHOUR, A. S. - ABD EL-MONSEF, M. E. - EL-DEEB, S. N., On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53. Zbl0571.54011MR830896
  21. MASHHOUR, A. S. - HASANEIN, I. A. - EL-DEEB, S. N., α-continuous and α-open mappings, Acta Math. Hungar., 41 (1983), 213-218. MR703734DOI10.1007/BF01961309
  22. NEUBRUNNOVÁ, A., On certain generalizations of the notion of continuity, Mat. Casopis, 23 (4) (1973), 374-380. MR339051
  23. NJASTAD, O., On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970. Zbl0137.41903MR195040
  24. NOIRI, T., On semi-continuous mappings, Lincei-Rend. Sc. fis. mat. e nat., 54 (1973), 210-214. MR350686
  25. NOIRI, T., On semi- T 2 spaces, Ann. Soc. Sci. Bruxelles, 90 (1976), 215-220. MR405348
  26. NOIRI, T., On S-closed spaces, Ann. Soc. Sci. Bruxelles, 91 (1977), 189-194. Zbl0408.54017MR474204
  27. NOIRI, T., On S-closed subspaces, Lincei-Rend. Sc. fis. mat. e nat., 64 (1978), 157-162. MR551642
  28. NOIRI, T., Semi-continuity and weak-continuity, Czechoslovak Mathematical Journal, 31(106) (1981), 314-321. Zbl0483.54006MR611084
  29. NOIRI, T., A function which preserves connected spaces, Cas. pest. mat., 107 (1982), 393-396. Zbl0511.54008MR683820
  30. NOIRI, T., On a-continuous functions, Cas. pest. mat., 109 (1984), 118-126. Zbl0544.54009MR744869
  31. PIOTROWSKI, Z., On semi-homeomorphisms, Boll. Un. Mat. Ital., (5) 16-A (1979), 501-509. Zbl0424.54002MR551374
  32. PIPITONE, V. - RUSSO, G., Spazi semiconnessi a spazi semiaperti, Rend. Circ. Mat. Palermo, 24 (2) (1975), 273-285. MR464149DOI10.1007/BF02843735
  33. REILLY, I. L. - VAMANAMURTHY, M. K., Connectedness and strong semi-continuity, Čas. pěst. mat., 109 (1984), 261-265. C Zbl0553.54005MR755590
  34. ROSE, D. A., Weak openness and almost openness, Internat. J. Math. and Math. Sci., 7(1) (1984), 35-40. Zbl0562.54020MR743822DOI10.1155/S0161171284000041
  35. ROSE, D. A., Weak continuity and almost continuity, Internat. J. Math. and Math. Sci., 7(2) (1984), 311-318. Zbl0552.54007MR757276DOI10.1155/S0161171284000338
  36. SINGAL, M. K. - SINGAL, ASHA RANI, Almost-continuous mappings, Yokohama Math. J., 16 (1968), 63-73. Zbl0191.20802MR261569
  37. SIVARAJ, D., I-compact subsets, Boll. Un. Mat. Ital., (6) 3-B (1984), 87-98. MR744431
  38. SOUNDARARAJAN, T., 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. MR283746
  39. TADROS, S. F., KHALAF, A. B., On regular semi-open sets and s*-closed spaces, Tamkang J. Math., 23(4) (1992), 337-348. Zbl0780.54020MR1204644
  40. THOMPSON, T., S-closed spaces, Proc. Amer. Math. Soc., 60 (1976), 335-338. MR425899DOI10.2307/2041169
  41. WILANSKY, A., Topics in functional analysis, Lecture Notes in Mathematics, vol. 45, Springer-Verlag1967. Zbl0156.36103MR223854

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