52 citations · 158 across the 14 of their papers we have counts for
14 papers
Topology on diffeological vector spaces
Enxin Wu, Zhongqiang Yang
It is expected that the -topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector s…
Pushforward and smooth vector pseudo-bundles
Enxin Wu
In this paper, we study a new operation named pushforward on diffeological vector pseudo-bundles, which is left adjoint to the pullback. We show how to pushforward projective diffe…
Exterior bundles in diffeology
J. Daniel Christensen, Enxin Wu
We explore several notions of -form at a point in a diffeological space, construct bundles of such -forms, and compare sections of these bundles to differential forms. As the…
Smooth classifying spaces
J. Daniel Christensen, Enxin Wu
We develop the theory of smooth principal bundles for a smooth group , using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bun…
Diffeological vector spaces
J. Daniel Christensen, Enxin Wu
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functi…
The Fermat Functors, Part I: The theory
Enxin Wu
In this paper, we use some basic quasi-topos theory to study two functors: one adding infinitesimals of Fermat reals to diffeological spaces (which generalize smooth manifolds incl…
Convergences and the Intermediate Value Property in Fermat Reals
Enxin Wu
This paper contains two topics of Fermat reals, as suggested by the title. In the first part, we study the ω-topology, the order topology and the Euclidean topology on Fermat reals…
Tangent spaces of bundles and of filtered diffeological spaces
J. Daniel Christensen, Enxin Wu
We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filt…
Calculus in the ring of Fermat reals Part I: Integral calculus
Paolo Giordano, Enxin Wu
We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Bes…
Tangent spaces and tangent bundles for diffeological spaces
J. Daniel Christensen, Enxin Wu
We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces a…
Homological Algebra for Diffeological Vector Spaces
Enxin Wu
Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially f…
Categorical frameworks for generalized functions
Paolo Giordano, Enxin Wu
We tackle the problem of finding a suitable categorical framework for generalized functions used in mathematical physics for linear and non-linear PDEs. We are looking for a Cartes…
The homotopy theory of diffeological spaces
J. Daniel Christensen, Enxin Wu
Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smoot…
The D-topology for diffeological spaces
J. Daniel Christensen, Gord Sinnamon, Enxin Wu
Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural…