Ps-normal and Ps-Tychonoff spaces

Abstract

A space X is called Ps-normal(Ps-Tychonoff) space if there exists a normal(Tychonoff) space Y and a bijection \(f: X\mapsto Y\) such that \(f|_K:K\mapsto f(K)\) is homeomorphism for any pseudocompact subset K of X. We establish a few relations between C-normal, CC-normal, L-normal, C-Tychonoff, CC-Tychonoff spaces with Ps-normal and Ps-Tychonoff spaces.

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References

  1. 1.

    AlZahrani, S.: \(C\)-Tychonoff and \(L\)-Tychonoff topological spaces. Eur. J. Pure Appl. Math. 11, 882–892 (2018)

    MathSciNet  Article  Google Scholar 

  2. 2.

    AlZahrani, S., Kalantan, L.: \(C\)-normal topological property. Filomat 31, 407–411 (2017)

    MathSciNet  Article  Google Scholar 

  3. 3.

    Engelking, R.: General Topology. Sigma Series in Pure Mathematics. Heldermann, Berlin (1989)

    Google Scholar 

  4. 4.

    Hewitt, E.: Rings of real valued continuous functions. I. Trans. Am. Math. Soc. 64, 45–99 (1948)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Kalantan, L., Alhomieyed, M.: \(CC\)-normal topological spaces. Turk. J. Math. 41, 749–755 (2017)

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank to Professor Sudip Kumar Acharyya and Professor Asit Baran Raha for their valuable suggestions. The authors also wish to thank the learned referee for his/her suggestions that improved the article.

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Correspondence to Sagarmoy Bag.

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The first author thanks the NBHM, Mumbai-400 001, India, for financial support. The second author thanks to Government of West Bengal, India, for financial support.

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Bag, S., Manna, R.C. & Patra, S.K. Ps-normal and Ps-Tychonoff spaces. Afr. Mat. 31, 589–594 (2020). https://doi.org/10.1007/s13370-019-00744-6

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Keywords

  • Ps-Tychonoff
  • C–Tychonoff
  • L-Tychonoff
  • Ps-normal
  • C-normal
  • CC-normal

Mathematics Subject Classification

  • Primary 54C40
  • Secondary 46E25