Space with Euler characteristic one

Definition
Suppose $$X$$ is a topological space that is a defining ingredient::space with finitely generated homology, i.e., it has only finitely many nontrivial homology groups and all of them are finitely generated. We say that $$X$$ is a space with Euler characteristic one if the defining ingredient::Euler characteristic of $$X$$ equals $$1$$, i.e., $$\chi(X) = 1$$.