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This book describes concept of generalized continuity and generalized separation axioms in fine topological space. The collection of fine-open sets contains all semi-open, pre-open, α-open, β-open etc. sets which are used to define the generalized concepts of continuity which includes several continuities already defined. The fine-topological space is a special class of generalized topological space which is based on a topological space. The concept of continuity and homeomorphism are used in many fields such as in Quantum physics, Quantum mechanics, computer science, chemistry, physics etc.

This book describes a new concept of fine topological space. The collection of fine open sets contains all semi-open, pre-open, -open, -open etc. sets which are used in defining the lighter concepts of continuity. With this wider class of fine sets the authors have defined the continuity which includes several other continuities already defined. Csaszar A. has introduced the concept of generalized topological space in 2002. A fine topological space is a special case of generalized topological space, but it may be noted that the concept of fine space is based on a topological space. The...