A generalized approach towards normality for topological spaces
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A uniform study towards normality is provided for topological spaces. Following Cs\'{a}sz\'{a}r, $\gamma$-normality and $\gamma$($\theta$)-normality are introduced and investigated. For $\gamma \in \Gamma_{13}$, $\gamma$-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as $\theta$-normality, $\Delta$-normality etc. are shown to be particular cases of $\gamma$($\theta$)-normality. In this process, $\gamma$-regularity and $\gamma$($\theta$)-regularity are introduced and studied. Several important characterizations of all these notions are provided.
Abstract
A uniform study towards normality is provided for topological spaces. Following Cs\'{a}sz\'{a}r, $\gamma$-normality and $\gamma$($\theta$)-normality are introduced and investigated. For $\gamma \in \Gamma_{13}$, $\gamma$-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as $\theta$-normality, $\Delta$-normality etc. are shown to be particular cases of $\gamma$($\theta$)-normality. In this process, $\gamma$-regularity and $\gamma$($\theta$)-regularity are introduced and studied. Several important characterizations of all these notions are provided.
참고문헌 (11)
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