Escrever uma avaliação PREreview

Recently, Abbas introduced the notion of an h-open set as a class of generalized open sets in a topological space. The subsequent corrigendum and addendum of Sharma, Saproo, Billawria and Digra clarified the theory and established that the family of all h-open sets is itself a topology, denoted by τh, without any T1/2 assumption. Motivated by this topological interpretation, we introduce and study the separation axioms h-D1 and h-D2 by means of h-difference sets. We prove that these two axioms coincide, relate them to the classical Di axioms in the associated topology (X, τh), examine their interaction with h-Ti and h-symmetric spaces, and obtain preservation results under h-irresolute and h-continuous mappings. Finite and infinite examples are included to distinguish the original topology from the associated topology of h-open sets. We also correct the overly strong assertion that h-symmetry alone implies h-T1: the additional h-T0 hypothesis is essential. In addition, we place the h-R0, h-RH and h-RD conditions in the associated-topology framework, establish a compatible subspace theorem, and clarify the interaction between h-compactness and h-T2. Three vector diagrams summarize the structural relationships among the separation axioms considered.