Product of real projective plane and circle

Definition
This topological space is defined as the product of the defining ingredient::real projective plane $$\R\mathbb{P}^2$$ and the defining ingredient::circle $$S^1$$ (note that $$S^1$$ is homeomorphic to $$\R\mathbb{P}^1$$). it is denoted $$\R\mathbb{P}^2 \times S^1$$.

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

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