Let X be a topological space, and let C(X) be the complex of singular cochains on X with coefficients in R. We denote by C c (X) (resp. C ∗ b (X)) the subcomplex of C(X) given by continuous (resp. locally bounded Borelian) cochains, i.e. by such cochains whose restriction to the space of simplices (endowed with the compact-open topology) defines a continuous (resp. locally bounded Borelian) rea...

A short proof of the fact that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms is given. It is not required that manifolds are second countable or paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.

Throughout the sequel, E denotes a reflexive real Banach space and E∗ its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with ‖x‖ = 1, and each > 0, there exists δ > 0 such that, for every y ∈ E satisfying ‖y‖ = 1 and ‖x− y‖ ≥ , one has ‖x + y‖ ≤ 2(1 − δ). Recall that any reflexive Banach space admits an equivalent norm with which it is loca...

Abstract In this paper, we introducing fuzzy neutrosophic supra first countable (FNS - FCS), second (FNS- SCS) and compactness compactness), Q μ compactness) in topological space (FNSTS). derive the union of two FNS – compact spaces is also similarly space. Also define some theorems using finite intersection property productive property. Finally observe that our notions preserve under one one, ...

Abstract In Continuum Light Cone Quantization (CLCQ) the treatment of scalar fields as operator valued distributions and properties of the accompanying test functions are recalled. Due to the paracompactness property of the Euclidean manifold these test functions appear as decomposition of unity. The approach is extended to QED Dirac fields in a gauge invariant way. With such test functions the...