A New type of Connected Sets via Bioperations

Ibrahim, Hariwan Z.

doi:10.28924/2291-8639-16-2018-518

Research Article

A New type of Connected Sets via Bioperations

Hariwan Z. Ibrahim¹

University of Zakho

Abstract

The purpose of this paper is to introduce the notion of $\alpha_{(\gamma, \gamma^{'})}$-separated sets and study their properties in topological spaces, then we introduce the notions of $\alpha_{(\gamma, \gamma^{'})}$-connected and $\alpha_{(\gamma, \gamma^{'})}$-disconnected sets. We discuss the characterizations and properties of $\alpha_{(\gamma, \gamma^{'})}$-connected sets and then properties under $(\alpha_{(\gamma, \gamma^{'})}$, $\alpha_{(\beta, \beta^{'})})$-continuous functions. The $\alpha_{(\gamma, \gamma^{'})}$-components in a space $X$ is also introduced.

How to Cite

H. Z. Ibrahim, A New type of Connected Sets via Bioperations, Int. J. Anal. Appl. 16 (2018), 518–527. https://doi.org/10.28924/2291-8639-16-2018-518

BibTeX

@article{Ibrahim2018,
  author  = {Ibrahim, Hariwan Z.},
  title   = {A New type of Connected Sets via Bioperations},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {518--527},
  doi     = {10.28924/2291-8639-16-2018-518}
}

References

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[2] H. Z. Ibrahim, On α (γ,γ 0 ) -open sets in topological spaces, (submitted).
[3] H. Z. Ibrahim, On (α (γ,γ 0 ) , α (β,β 0 ) )-functions, (submitted).
[4] S. Mishra, On α-Ï„-disconnectedness and α-Ï„-connectedness in topological spaces, Acta Sci., Technol., 37 (3) (2015), 395-399.
[5] O. Njastad, On some classes of nearly open sets, Pac. J. Math. 15 (1965), 961-970.