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Published online by Cambridge University Press: 06 July 2010
In this chapter we introduce the basic definitions and elementary properties of foliated spaces.
The local picture of a foliated space is a topological space of the form L×N, where L is a copy of ℝp and N is a separable metric space, not necessarily a manifold. A tangentially smoothfunction
f: L×N → ℝ
is a continuous function with the following properties:
(1) For each n ∈ N, the function f(·, n) L→ ℝ is smooth.
(2) All partial derivatives of f in the L directions are continuous on L × N.
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