A point calculus for interlevel set homology
The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology. (c) 2011 Elsevier B.V. All rights reserved.
interlevel sets homology continuous functions vector spaces persistence diagrams exact sequences