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Locally $ P$-closed spaces and rim $ P$-closed spaces


Author: Dix H. Pettey
Journal: Proc. Amer. Math. Soc. 87 (1983), 543-548
MSC: Primary 54D25; Secondary 54C15
DOI: https://doi.org/10.1090/S0002-9939-1983-0684655-2
MathSciNet review: 684655
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Abstract: It is shown in this paper that for $ P = {T_2}$ or $ P = {T_3}$ every locally $ P$-closed space is a retract of a rim $ P$-closed, locally $ P$-closed space by an open, perfect retraction map. From this it follows that there exist noncompact, rim $ H$-closed, $ H$-closed spaces and noncompact, rim $ R$-closed, $ R$-closed spaces.


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  • [1] M. P. Berri, J. R. Porter and R. M. Stephenson, Jr., A survey of minimal topological spaces, General Topology and its Relation to Modern Analysis and Algebra. III, Proc. Kanpur Topology Conf. (1968), Academia, Prague, 1971, pp. 93-114. MR 0278254 (43:3985)
  • [2] Alan Dow and Jack Porter, Embedding in $ R$-closed spaces, Topology Appl. (to appear). MR 676965 (84a:54043)
  • [3] Ryszard Engelking, General topology, PWN, Warsaw, 1977. MR 0500780 (58:18316b)
  • [4] Louis M. Friedler and Dix H Pettey, Inverse limits and mappings of minimal topological spaces, Pacific J. Math. 71 (1977), 429-448. MR 0464158 (57:4093)
  • [5] F. Obreanu, Espaces localement absolument fermés, Ann. Acad. Repub. Pop. Romaine Sect. Sti. Fiz. Chim. Ser. A 3 (1950), 375-394. MR 0044825 (13:484a)
  • [6] Jack Porter, On locally $ H$-closed spaces, Proc. London Math. Soc. (3) 20 (1970), 193-204. MR 0256354 (41:1010)
  • [7] T. O. Vinson, Jr. and R. F. Dickman, Jr., Inverse limits and absolutes of $ H$-closed spaces, Proc. Amer. Math. Soc. 66 (1977), 351-358. MR 0482660 (58:2718)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0684655-2
Keywords: $ P$-closed space, locally $ P$-closed space, rim $ P$-closed space
Article copyright: © Copyright 1983 American Mathematical Society

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