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Keywords:
locally compact; ultracomplete; Čech-complete; countable character; boun\-ded set
locally compact; ultracomplete; Čech-complete; countable character; boun\-ded set
Summary:
In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space $X$ at which $X$ is not locally compact and call it an nlc set. In 1999, Garc'{\i}a-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces which have compact nlc sets are studied. Such spaces contain dense locally compact subspaces and coincide with ultracomplete spaces in the realms of normal $\gamma$-spaces or ks-spaces.
References:
[1] Buhagiar D.: Non locally compact points in ultracomplete topological spaces. Questions Answers Gen. Topology 19 (2001), 125-131. MR 1815353 | Zbl 0976.54025
[2] Buhagiar D., Yoshioka I.: Ultracomplete topological spaces. to appear in Acta Math. Hungar. 92 (2001). MR 1924245 | Zbl 0997.54037
[3] Buhagiar D., Yoshioka I.: Sums and products of ultracomplete spaces. to appear in Topology Appl. MR 1919293
[4] Chaber J.: Conditions which imply compactness in countably compact spaces. Bull. Acad. Pol. Sci. Ser. Math. 24 (1976), 993-998. MR 0515000
[5] Engelking R.: General Topology. Polish Sci. Publ., Warsaw, 1977. MR 0500780 | Zbl 0684.54001
[6] García-Máynez A., Romaguera S.: Perfectly pre-images of cofinally complete metric spaces. Comment. Math. Univ. Carolinae 40 (1999), 335-342. MR 1732655
[7] Henriksen M., Isbell J.R.: Some properties of compactifications. Duke Math. J. 35 (1958), 83-105. MR 0096196 | Zbl 0081.38604
[8] Hodel R.E.: Spaces defined by sequences of open covers which guarantee that certain sequences have cluster points. Duke Math. J. 39 (1972), 253-263. MR 0293580 | Zbl 0242.54027
[9] Howes N.R.: On completeness. Pacific J. Math. 38 (1971), 431-440. MR 0307183 | Zbl 0221.54027
[10] Lutzer D.J.: Semimetrizable and stratifiable spaces. Gen. Topology Appl. 1 (1971), 43-48. MR 0296893 | Zbl 0211.25704
[11] Michael E.A.: A quintuple quotient quest. Gen. Topology Appl. 2 (1972), 91-138. MR 0309045 | Zbl 0238.54009
[12] Nagata J.: Modern General Topology. North-Holland Math. Library, Amsterdam, 1985, second revised edition. MR 0831659 | Zbl 0598.54001
[13] Romaguera S.: On cofinally complete metric spaces. Questions Answers Gen. Topology 16 (1998), 165-170. MR 1642068 | Zbl 0941.54030
[14] Vaughan J.E.: Spaces of countable and point-countable type. Trans. Amer. Math. Soc. 151 (1970), 341-351. MR 0266157 | Zbl 0203.55403
[15] Yoshioka I.: On the metrizations of $\gamma$-spaces and ks-spaces. Questions Answers Gen. Topology 19 (2001), 55-72. MR 1815346 | Zbl 0983.54030
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