On compactifications with path connected remainders

Dijkstra, Jan

doi:10.1090/S0002-9939-08-09567-1

On compactifications with path connected remainders
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by Jan J. Dijkstra PDF

Proc. Amer. Math. Soc. 136 (2008), 4461-4466 Request permission

Abstract:

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon.

References

Ofelia T. Alas, Mikhail G. Tkačenko, Vladimir V. Tkachuk, and Richard G. Wilson, Connectifying some spaces, Topology Appl. 71 (1996), no. 3, 203–215. MR 1397942, DOI 10.1016/0166-8641(95)00012-7
Philip L. Bowers, Dense embeddings of nowhere locally compact separable metric spaces, Topology Appl. 26 (1987), no. 1, 1–12. MR 893799, DOI 10.1016/0166-8641(87)90021-6
F. H. Croom, Principles of Topology, Saunders, Philadelphia, 1989.
Eric K. van Douwen, Remote points, Dissertationes Math. (Rozprawy Mat.) 188 (1981), 45. MR 627526
A. Emeryk and W. Kulpa, The Sorgenfrey line has no connected compactification, Comment. Math. Univ. Carolinae 18 (1977), no. 3, 483–487. MR 461437
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
Gary Gruenhage, John Kulesza, and Attilio Le Donne, Connectifications of metrizable spaces, Topology Appl. 82 (1998), no. 1-3, 171–179. Special volume in memory of Kiiti Morita. MR 1602455, DOI 10.1016/S0166-8641(97)00067-9
Jan van Mill, The infinite-dimensional topology of function spaces, North-Holland Mathematical Library, vol. 64, North-Holland Publishing Co., Amsterdam, 2001. MR 1851014
Jack R. Porter and R. Grant Woods, Subspaces of connected spaces, Topology Appl. 68 (1996), no. 2, 113–131. MR 1374077, DOI 10.1016/0166-8641(95)00057-7
P. Simon, Two questions about connected compactifications, Topology Atlas (2003), http://at.yorku.ca/q/a/a/a/22.htm.
Stephen Watson and Richard G. Wilson, Embeddings in connected spaces, Houston J. Math. 19 (1993), no. 3, 469–481. MR 1242433