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Some Results on Pixley–Roy Hyperspaces

Author

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  • LjubiÅ¡a D. R. KoÄ inac
  • Luong Quoc Tuyen
  • Ong Van Tuyen
  • A. Ghareeb

Abstract

In this paper, we prove that if a space X has a point-countable cn-network, then the Pixley-Roy hyperspace PRX also has a point-countable cn-network. If X is a regular space with a point-countable ck-network, then so does the Pixley-Roy hyperspace PRX. Moreover, if X has a point-countable sp-network (resp., strict Pytkeev network), then the Pixley–Roy hyperspace PR2X also has a point-countable sp-network (resp., strict Pytkeev network). On the other hand, we show that if the Pixley–Roy hyperspace PRX has a countable cn-network (resp., sp-network and strict Pytkeev network), then so does X. By these results, we obtain that if the Pixley–Roy hyperspace PRX is a cosmic space (resp., P0-space, strict P0-space, and stric P0-space), then so is X. Furthermore, the Pixley-Roy hyperspace PRnS2 is not a k-space for each n≥2.

Suggested Citation

  • LjubiÅ¡a D. R. KoÄ inac & Luong Quoc Tuyen & Ong Van Tuyen & A. Ghareeb, 2022. "Some Results on Pixley–Roy Hyperspaces," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, March.
    • Handle: RePEc:hin:jjmath:5878044
    DOI: 10.1155/2022/5878044
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