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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.
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참고문헌 (11)
참고문헌 신청
M. E. Abd EI-Monsef / 1983 / β - open sets and β - continuous mappings / Bull. Fac. Sci. Assiut Univ 12:77~90
A. Csaszar / 1997 / Generalized open sets / Acta Math. Hungar 75(1-2):65~87
A. K. Das / 2009 / Δ-normal spaces and decompositions of normality / App. Gen. Top 10(2):197~206
Dickman, R. F., Jr / 1977 / θ-perfect and θ-absolutely closed functions / Illinois J. Math 21(1):42~60
J. Dugundji / 1972 / Topology / Allyn and Bacon
A. Csaszar / 1997 / Generalized open sets / Acta Math. Hungar 75(1-2):65~87
A. K. Das / 2009 / Δ-normal spaces and decompositions of normality / App. Gen. Top 10(2):197~206
Dickman, R. F., Jr / 1977 / θ-perfect and θ-absolutely closed functions / Illinois J. Math 21(1):42~60
J. Dugundji / 1972 / Topology / Allyn and Bacon
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