Locally 𝑃-closed spaces and rim 𝑃-closed spaces

Pettey, Dix H.

doi:10.1090/S0002-9939-1983-0684655-2

Locally $P$-closed spaces and rim $P$-closed spaces
HTML articles powered by AMS MathViewer

by Dix H. Pettey PDF

Proc. Amer. Math. Soc. 87 (1983), 543-548 Request permission

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.

References

M. P. Berri, J. R. Porter, and R. M. Stephenson Jr., A survey of minimal topological spaces, General Topology and its Relations to Modern Analysis and Algebra, III (Proc. Conf., Kanpur, 1968) Academia, Prague, 1971, pp. 93–114. MR 0278254
Alan Dow and Jack Porter, Embedding in $R$-closed spaces, Topology Appl. 15 (1983), no. 1, 45–58. MR 676965, DOI 10.1016/0166-8641(83)90046-9
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
Louis M. Friedler and Dix H. Pettey, Inverse limits and mappings of minimal topological spaces, Pacific J. Math. 71 (1977), no. 2, 429–448. MR 464158, DOI 10.2140/pjm.1977.71.429
Filip Obreanu, Espaces localement absolument fermés, An. Acad. Repub. Pop. Române. Secţ. Şti. Mat. Fiz. Chim. Ser. A. 3 (1950), 375–394 (Romanian, with Russian and French summaries). MR 0044825
Jack Porter, On locally $H$-closed spaces, Proc. London Math. Soc. (3) 20 (1970), 193–204. MR 256354, DOI 10.1112/plms/s3-20.2.193
T. O. Vinson Jr. and R. F. Dickman Jr., Inverse limits and absolutes of $H$-closed spaces, Proc. Amer. Math. Soc. 66 (1977), no. 2, 351–358. MR 482660, DOI 10.1090/S0002-9939-1977-0482660-X