Some aspects of cosheaves on diffeological spaces

A Tangent Bundle on Diffeological Spaces

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

The homotopy theory of diffeological spaces

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 smooth homotopy groups that we will need later. Then we introduce the smooth singular simplicial set S(X) associated to a diffeological space X, and show that when S(X) is fibrant, it captures smooth homotopical properties...

Happy Fractals and Some Aspects of Analysis on Metric Spaces

There has been a lot of interest and activity along the general lines of “analysis on metric spaces” recently, as in [2], [3], [26], [40], [41], [46], [48], [49], [51], [82], [83], [89], for instance. Of course this is closely related to and involves ideas concerning “spaces of homogeneous type”, as in [18], [19], [66], [67], [92], as well as subRiemannian spaces, e.g., [8], [9], [34], [47], [5...

Partial Inner Product Spaces: Some Categorical Aspects

Basic Forms and Orbit Spaces: a Diffeological Approach

If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential...