9 papers
On Reeb spaces of non-proper smooth functions which are -dimensional CW complexes
Naoki Kitazawa
We discuss Reeb spaces of non-proper smooth functions. (Non-)proper functions are maps between topological spaces the preimages of compact sets by which are compact (resp. may not…
Reeb spaces of 1st derivatives of proper submersions of certain classes
Naoki Kitazawa
We study the (canonical) 1st derivatives of {\it proper} submersions represented as height functions and belonging to a certain class: a proper map means a map the preimage of a co…
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-Bott functions with prescribed preimages on -dimensional manifolds and conditions for the reconstruction
Naoki Kitazawa
We present conditions for reconstruction of Morse-Bott functions with prescribed preimages on -dimensional manifolds. The present work strengthens a previous result for the Mors…
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…