7 papers
Compactifying real analytic functions and resulting Reeb spaces
Naoki Kitazawa
We formulate compactifications of continuous maps naturally. We consider real analytic functions mainly. We are interested in topological properties and combinatorial ones of expli…
Representations of Reeb spaces via simplified graphs and examples
Naoki Kitazawa
Reeb spaces of continuous real-valued functions on topological spaces are fundamental and strong tools in investigating the spaces. The Reeb space is the natural quotient space of…
Morse functions with regular level sets consisting of -dimensional spheres, -dimensional tori, or Klein Bottles
Naoki Kitazawa
In this paper, we study Morse functions with regular level sets consisting of spheres, tori, or Klein Bottles on -dimensional closed manifolds. We characterize -dimensional m…
Reeb spaces of smooth functions associated to globally similar graphs of smooth functions
Naoki Kitazawa
Previously, we have investigated a natural smooth map onto the region surrounded by the graphs of two smooth real-valued functions in the plane converging to a same value or diverg…
A note on asymptotic behaviors and topological properties of two smooth real-valued functions and several graphs associated to them
Naoki Kitazawa
This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical project…
On reconstructing Morse functions with prescribed level sets on -dimensional manifolds and a necessary and sufficient condition for the reconstruction
Naoki Kitazawa
We discuss a necessary and sufficient condition for reconstruction of Morse functions with prescribed (regular) level sets on -dimensional manifolds. The present work strengthen…