Preface
At the Beginning
Diffeology， the Axiomatic
The Irrational Tori 8
Generating Families， Dimension
Cartan-De-Rham Calculus
Diffeology Fiber Bundles
Homotopy Theory in Diffeology
Local Diffeology， Modeling
Modeling: Manifolds， Orbifolds and Quasifolds
Symplectic Mechanics and Diffeology
Diffeology and Non-Commutative Geometry
Functional Diffeology on Fourier Coefffcients
Smooth Function on Periodic Functions
Symplectic Diffeology on Smooth Periodic Functions
Infinite Torus Action on Smooth Periodic Functions
Basic 1-Forms on Principal Fiber Bundles
Differential of Holonomy for Torus Bundles
Non-symplectic manifold with injective univ. moment map
On Riemannian Metric in Diffeology
A Few Half-Lines
1-Forms on Half-Lines
1-Forms on the Subset Half-Line
Cotangent Space of the Half-Line
1-Forms on Half-Spaces
p-Forms on Half-Spaces
p-Forms on Corners
Differential Forms on the Cross
A note on Hamiltonian Diffeomorphisms
Differential of a Lie-Group Valued Function
The Geodesics of the 2-Torus
The Use of the Moment Map in Geodesic Calculus
The Parasymplectic Space of Geodesics Trajectories
Diffeomorphisms of Geod(T2)
The Diffeomorphisms of the Square
Diffeological Spaces are Locally Connected
Vague Adjunction of a Point to a Space
Embedding a Diffeological Space Into its Powerset
Foliations and Diffeology
Klein Stratiffcation of Diffeological Spaces
Lagrange’s Equations of Motion
Poisson Bracket in Diffeology
Smooth embeddings and smoothly embedded subsets
Seifert Orbifolds
Symplectic spaces without Hamiltonian diffeomorphisms
The Diffeology Framework of General Covariance
Postface: The Beginning of Diffeological Spaces
Appendix: A Categorical Approach to Diffeology
Bibliography
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