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τ-Pseudocompact Mappings

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Abstract

We consider the problem of extending the notion of τ-pseudocompactness from spaces to continuous mappings, obtain conditions under which the product of τ-pseudocompact mappings is τ-pseudocompact. Since any space X can be considered as a continuous mapping from X into a singleton, we obtain consequences of the theorems on multiplicativity of τ-pseudocompactness for spaces. Thus, we study the notion of τ-pseudocompact mapping and some its properties similar to those of a pseudocompact space as well as consequences of the obtained assertions for spaces.

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References

  1. Comfort W. and Kenneth A. R., “Pseudocompactness and uniform continuity in topological groups,” Pacific J. Math., 16, No. 3, 483–496 (1966).

    Google Scholar 

  2. Tkachenko M. G., “Generalization of the Comfort-Ross theorem. I,” Ukrain. Mat. Zh., 41, No. 3, 377–382 (1989).

    Google Scholar 

  3. Uspenski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{i} \) V. V., “Topological groups and the Dugundji compacta,” Mat. Sb., 180, No. 8, 1092–1118 (1989).

    Google Scholar 

  4. Tkachenko M. G., “Generalization of the Comfort–Ross theorem. II,” Ukrain. Mat. Zh., 41, No. 7, 939–952 (1989).

    Google Scholar 

  5. Mironova Yu. N., “Multiplicativity of relative τ pseudocompactness,” in: General Topology. Mappings, Products, and Dimension of Spaces, Moscow Univ., Moscow, 1994, pp. 77–82.

    Google Scholar 

  6. Mironova Yu. N., “Properties of o-pseudocompact mappings,” in: Abstracts: VI International Conference ofWomen-Mathematicians: Mathematics. Education. Economics, Cheboksary, May 25–30, 1998, Cheboksary, 1998, p. 54.

  7. Aleksandrov P. S. and Pasynkov B. A., An Introduction to Dimension Theory [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  8. Pasynkov B. A., “On translation to mappings of some notions and statements concerning spaces,” in: Mappings and Functors [in Russian], Moscow Univ., Moscow, 1984, pp. 77–82.

    Google Scholar 

  9. Buzulina T. I. and Pasynkov B. A., “On Dieudonné complete mappings,” in: Geometry of Immersed Manifolds [in Russian], Moscow Ped. Inst., Moscow, 1989, pp. 95–99.

    Google Scholar 

  10. Il'ina N. I. and Pasynkov B. A., “On R-complete mappings,” in: Geometry of Immersed Manifolds [in Russian], Moscow Ped. Inst., Moscow, 1989, pp. 125–131.

    Google Scholar 

  11. Engelking R., General Topology [Russian translation], Mir, Moscow (1986).

    Google Scholar 

  12. Arkhangel'ski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{i} \); A. V., “Free topological groups: state of the art and problems,” in: Abstracts: Baku International Topological Conference, Baku, 1987, p. 18.

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  1. Moscow State Law Academy, Moscow

    Yu. N. Mironova

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  1. Yu. N. Mironova
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Mironova, Y.N. τ-Pseudocompact Mappings. Siberian Mathematical Journal 42, 537–545 (2001). https://doi.org/10.1023/A:1010427310849

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  • DOI: https://doi.org/10.1023/A:1010427310849

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