4 papers
The Zariski Cotangent Space at the Origin of the Pencil Diffeological Space
Masaki Taho
The pencil diffeological space is a plane whose smooth structure at the origin is detected only along lines through it. We show that the Zariski cotangent space at the origin is en…
Topology and Diffeology via Metric-like Functions
Masaki Taho
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniform…
Diffeological Spaces with a Non-Smooth Derivation
Masaki Taho
We show that on certain diffeological spaces there exist linear derivations that satisfy the Leibniz rule but are not smooth with respect to the given diffeology. This reveals that…
Infinitely Many Tangent Functors on Diffeological Spaces
Masaki Taho
We study tangent spaces in the setting of diffeological spaces. Several distinct tangent functors have been introduced, each of which extends the classical tangent functor from smo…