A new generalization of normality called almost β-normality is introduced and studied which is a simultaneous generalization of almost normality and β-normality. A topological space is called almost β-normal if for every pair of disjoint closed sets A and B one of which is regularly closed, there exist disjoint open sets U
In [1], the authors prove that almost β-normality is preserved by continuous, open, closed surjections. We present examples to show that neither "open" nor "closed" can be omitted.
A simultaneous generalization of κ-normality and weak θ-normality is introduced. Interrelation of this generalization of normality with existing variants of normality is studied. In the process of investigation a new decomposition of normality is obtained.2010 MSC: Primary 54D10; 54D15; Secondary 54D20.
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