Mapping theorems on mesocompact spaces
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- by Kuo Shih Kao and Li Sheng Wu PDF
- Proc. Amer. Math. Soc. 89 (1983), 355-357 Request permission
Abstract:
In this paper we prove two mapping theorems on mesocompact spaces: (1) Perfect mappings preserve mesocompactness; (2) Closed mappings preserve normal mesocompactness.References
- Richard Arens and J. Dugundji, Remark on the concept of compactness, Portugal. Math. 9 (1950), 141–143. MR 38642
- A. V. Arhangel′skiĭ, Intersection of topologies, and pseudo-open bicompact mappings, Dokl. Akad. Nauk SSSR 226 (1976), no. 4, 745–748 (Russian). MR 0402671
- Philip Bacon, The compactness of countably compact spaces, Pacific J. Math. 32 (1970), 587–592. MR 257975
- James R. Boone, Some characterizations of paracompactness in $k$-spaces, Fund. Math. 72 (1971), no. 2, 145–153. MR 295291, DOI 10.4064/fm-72-2-145-153
- James R. Boone, A note on mesocompact and sequentially mesocompact spaces, Pacific J. Math. 44 (1973), 69–74. MR 315662
- James R. Boone, On $k$-quotient mappings, Pacific J. Math. 51 (1974), 369–377. MR 358665
- J. Chaber, Metacompactness and the class MOBI, Fund. Math. 91 (1976), no. 3, 211–217. MR 415561, DOI 10.4064/fm-91-3-211-217
- Heikki J. K. Junnila, Metacompactness, paracompactness, and interior-preserving open covers, Trans. Amer. Math. Soc. 249 (1979), no. 2, 373–385. MR 525679, DOI 10.1090/S0002-9947-1979-0525679-9
- Heikki J. K. Junnila, Paracompactness, metacompactness, and semi-open covers, Proc. Amer. Math. Soc. 73 (1979), no. 2, 244–248. MR 516472, DOI 10.1090/S0002-9939-1979-0516472-7
- V. J. Mancuso, Mesocompactness and related properties, Pacific J. Math. 33 (1970), 345–355. MR 264607
- E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173–176. MR 177396, DOI 10.1007/BF02759940 —, ${\aleph _0}$-spaces, J. Math. Mech. 15 (1966), 983-1002.
- Frank Siwiec and Vincent J. Mancuso, Relations among certain mappings and conditions for their equivalence, General Topology and Appl. 1 (1971), no. 1, 33–41. MR 282347
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 355-357
- MSC: Primary 54D20; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712651-5
- MathSciNet review: 712651