Preliminaries from differential topology and microlocal analysis
Vesselin M. Petkov · 2016
This chapter discusses some facts concerning manifolds of jets, spaces of smooth maps and transversality, as well as some material from microlocal analysis. A special emphasis is given to the definition and main properties of the generalized bicharacteristics of the wave operator and the corresponding generalized geodesics. The chapter also considers C∞ (X, Y ) with the Whitney C∞ topology. An important fact about these spaces, which will be often used in what follows, is that whenever X and Y are smooth manifolds, the space C∞(X, Y ) is a Baire topological space. Recall that a subset R of a topological space Z is called residual in Z if R contains a countable intersection of open dense subsets of Z. If every residual subset of Z is dense in it, then Z is called a Baire space.