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A note onR 1-topological spaces

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Abstract

The purpose of the present note is to give a number of characterizations of theR 1-axiom and to show that theR 1-axiom is equivalent to the weakly Hausdorff axiom introduced byB. Banaschewski andJ. M. Maranda [2]. In anR 1-space it is shown that the locally compactness property is also open hereditary and that the closure of an almost compact set is the union of the closures of its points. A necessary and sufficient condition is obtained under which a locally compact set dense in anR 1-space is open. Finally a variant of a well-known theorem regarding two continuous functions of a topological space into aT 2-space is formulated forR 1-spaces.

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References

  1. C. E. Aull andW. J. Thron, Separation axioms betweenT 0 andT 1,Indag. Math. 24 (1962), 26–27.MR 25 # 1529

    Google Scholar 

  2. B. Banaschewski andJ. M. Maranda, Proximity functions,Math. Nachr. 23 (1961), 1–37.MR 29 # 2768

    Google Scholar 

  3. Y. K. Choudhary andB. C. Singhai, Normality axioms,Rev. Un. Mat. Argentina 24 (1969), 155–158.MR 41 # 9180

    Google Scholar 

  4. Á. Császár,General topology, Akadémiai Kiadó, Budapest, and Hilger, Bristol, 1978.MR 57 # 13812

    Google Scholar 

  5. A. S. Davis, Indexed system of neighbourhoods for general topological spaces,Amer. Math. Monthly 68 (1961), 886–893.MR 35 # 4869

    Google Scholar 

  6. K. K. Dube, A note onR 0-topological spaces,Mat. Vesnik 11 (1974), 203–208.MR 51 # 13982

    Google Scholar 

  7. M. G. Murdeshwar andS. A. Naimpally,R 1-topological spaces,Canad. Math. Bull. 9 (1966), 521–523.MR 35 # 4870

    Google Scholar 

  8. M. G. Murdeshwar andS. A. Naimpally,Quasi-uniform topological spaces, Noordhoff, Groningen, 1966.MR 35 # 2267

    Google Scholar 

  9. I. L. Reilly,On essentially pairwise Hausdorff spaces, Auckland University, New Zealand, 1973. (Preprint)

    Google Scholar 

  10. I. L. Reilly, On essentially pairwise Hausdorff spaces,Rend. Circ. Mat. Palermo 25 (1976), 47–52.Zbl 374. 54025

    Google Scholar 

  11. G. D. Richardson,R 1 pairwise compact and pairwise complete spaces,Canad. Math. Bull. 15 (1972), 109–113.MR 47 # 4224

    Google Scholar 

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  1. Department of Mathematics and Statistics, University of Saugar, Sagar, M. P, India

    K. K. Dube

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  1. K. K. Dube
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Dube, K.K. A note onR 1-topological spaces. Period Math Hung 13, 267–271 (1982). https://doi.org/10.1007/BF01849239

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  • DOI: https://doi.org/10.1007/BF01849239

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