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Proceedings of the American Mathematical Society

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On unions of $ \nu $-embedded sets


Author: Hidenori Tanaka
Journal: Proc. Amer. Math. Soc. 79 (1980), 474-476
MSC: Primary 54C45; Secondary 54D60
DOI: https://doi.org/10.1090/S0002-9939-1980-0567996-6
MathSciNet review: 567996
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Abstract: Let A be a realcompact and C-embedded subspace of a space X and let B be a v-embedded subspace of a space X. Then $ A \cup B$ is v-embedded in X.


References [Enhancements On Off] (What's this?)

  • [1] Robert L. Blair, On 𝜐-embedded sets in topological spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Springer, Berlin, 1974., pp. 46–79. Lecture Notes in Math., Vol. 378. MR 0358677
  • [2] Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
  • [3] Akio Kato, Union of realcompact spaces and Lindelöf spaces, Canad. J. Math. 31 (1979), no. 6, 1247–1268. MR 553159, https://doi.org/10.4153/CJM-1979-104-8

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567996-6
Keywords: Hewitt realcompactification, C-embedded, $ {C^ \ast }$-embedded, z-embedded, v-embedded
Article copyright: © Copyright 1980 American Mathematical Society