Product of two real projective planes

Definition
This topological space is defined as the Cartesian product, equipped with the defining ingredient::product topology, of two copies of the defining ingredient::real projective plane $$\R\mathbb{P}^2$$. It is denoted $$\R\mathbb{P}^2 \times \R\mathbb{P}^2$$.

Homology groups
The homology groups with coefficients in integers are as follows:

$$H_p(\R\mathbb{P}^2 \times \R\mathbb{P}^2;\mathbb{Z}) = \left\lbrace \begin{array}{rl} \mathbb{Z}, & p = 0 \\ \mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}, & p = 1\\ \mathbb{Z}/2\mathbb{Z}, & p = 2,3 \\ 0, & p \ge 4 \\\end{array}\right.$$

These are computed using the homology of real projective space and the Kunneth formula.