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Product spaces and semi-separation axioms

Abstract

In this paper new characterizations of semi-R0 and semi-R1 spaces are obtained and used to prove that the product space of semi-R0, semi-T1, and semi-T0 spaces is, respectively, semi-R0, semi-T1, and semi-T0; and that the product space of semi-R1 space need not be semi-R1. An example is given where the product space is semi-T2 and one of the factor spaces is not semi-T0 or semi-R0.

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References

  1. [1]

    N. Biswas, On characterizations of semi-continuous functions,Atti Acad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 399–402.MR 44 # 998

  2. [2]

    Ch. Dorsett, Semi-T2, semi-R1 and semi-R0 topological spaces,Ann. Soc. Sci. Bruxelles Sér. I,92 (1978), 143–150.MR 80 a:54026

  3. [3]

    Ch. Dorsett, T2, R1 and semi-R1 spaces,Kyungpook Mathematical Journal 19 (1980), 159–163.

  4. [4]

    N. Levine, Semi-open sets and semi-continuity in topological spaces,Amer. Math. Monthly 70 (1963), 36–41.MR 29 # 4025

  5. [5]

    S. N. Maheshwari, andR. Prasad, Some now separation axioms,Ann. Soc. Sci. Bruxelles Sér. I, 89 (1975), 395–402.MR 52 # 6660

  6. [6]

    S. N. Maheshwari andR. Prasad, On (R0) s -spaces,Portugal. Math. 34 (1975), 213–217.MR 53 # 14409

  7. [7]

    T. Noiri, On semi-continuous mappings,Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur. 54 (1973), 210–214.MR 50 # 3178

  8. [8]

    T. Noiri, On semi-T2 spaces,Ann. Soc. Sci. Bruxelles Sér. I,90 (1976), 215–220.MR 53 # 9142

  9. [9]

    S. Willard,General topology, Addison-Wesley, Reading (Mass.), 1970.MR 41 # 9173

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Dorsett, C. Product spaces and semi-separation axioms. Period Math Hung 13, 39–45 (1982). https://doi.org/10.1007/BF01848095

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AMS (MOS) subject classifications (1970)

  • Primary 54-10
  • Secondary 54-25

Key words and phrases

  • Semi-open
  • semi-R0
  • semi-R1
  • semi-T i (i = 0, 1, 2)