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math.GN2026
Fundamental examples of Reeb spaces of smooth functions defined from two graphs of smooth functions with same asymptotic behaviors
Naoki Kitazawa
Reeb spaces of (continuous) real-valued functions on (nice) topological spaces are the spaces whose underlying sets consist of all connected components (contours) of their level se…
math.GN2025
Smooth functions which are Morse on preimages of values not being local extrema and constructing natural functions of the class on connected sums of manifolds admitting these functions
Naoki Kitazawa
We discuss smooth functions which are Morse on preimages of values not being local extrema. We call such a function internally Morse or I-Morse. The Reeb graph of a smooth function…