A New type of Connected Sets via Bioperations

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Hariwan Z. Ibrahim, A New type of Connected Sets via Bioperations, Int. J. Anal. Appl., 16 (4) (2018), 518-527.

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Hariwan Z. Ibrahim

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.

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References

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