Geodesic
Remarks on Two Weak Forms of Continuity
Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 59-63

Voir la notice de l'article provenant de la source Cambridge University Press

New characterizations of weakly-continuous and θ-continuous functions are presented, and θ-continuity is applied to characterize H(i) spaces; a recent characterization of closed graph functions is utilized to characterize H-closed spaces. Noiri has shown that a function λ which is almost-continuous in the sense of Husain is weakly-continuous if cl(λ−1(W)) ⊂ λ−1(cl(W)) for all open W. It is established here that almost-continuity is superfluous in this statement.
DOI : 10.4153/CMB-1982-008-8
Mots-clés : 54C05, 54D25, θ-continuity, weak-continuity, H-closed spaces 
Espelie, M. Solveig; Joseph, James E. Remarks on Two Weak Forms of Continuity. Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 59-63. doi: 10.4153/CMB-1982-008-8
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[A-U] Alexandroff, P. and Urysohn, P., Zur théorie der topologischen raüme, Math Ann. 92 (1924), 258-266. Google Scholar

[E-J] Espelie, M. S. and Joseph, J. E., Some properties of 6-closure, Canadian Jour. Math. 33 (1981), 142-149. Google Scholar

[F] Fomin, S., Extensions of topological spaces, Ann. Math. 44 (1943), 491-480. Google Scholar

[H] Husain, T., Topology and Maps, Plenum, New York, 1977. Google Scholar

[H-L] Hamlett, T. R. and Long, Paul E., Inverse cluster sets, Proc. Amer. Math. Soc. 53 (1975), 470-476. Google Scholar

[He-L]Herrington, L. L. and Long, P. E., Characterizations of H-closed spaces, Proc. Amer. Math. Soc. 48 (1975), 469-475. Google Scholar

[J] Joseph, J. E., Multifunctions and graphs, Pacific J. Math. 79 (1978), 509-529. Google Scholar

[J] Joseph, J. E., Multifunctions and cluster sets, Proc. Amer. Math. Soc. 74 (1979), 329-337. Google Scholar

[L] Norman, Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44-46. Google Scholar

[N] Noiri, T., On weakly continuous mappings, Proc. Amer. Math. Soc. 46 (1974), 120-124. Google Scholar

[N] Noiri, T., Weak-continuity and graphs, Casopis Pest. Mat. 101 (1976), 379-382. Google Scholar

[R] Rose, D. A., On Levine's decomposition of continuity, Canad. Math. Bull. Vol. 21 (4) (1978), 477-481. Google Scholar

[T]Thompson, T., Concerning certain subjects of non-Hausdorff topological spaces, Boll. U.M.I. (5) 14-A (1977), 34-37. Google Scholar

[V] Veličko, N. V., H-closed topological spaces, Mat. Sb., 70 (112) (166), 98-112; Amer. Math. Soc. Transi. 78 (Series 2) (1969), 103-118. Google Scholar

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