Prove $\sigma :\mathbb{F}^{2} \hookrightarrow \mathbb{FP}^{2};\, (x,y) \mapsto (x:y:1)$ is a homeomorphism onto its image

Question

I am trying to prove that the maps that embeds $\mathbb{F}^{2}$ into $\mathbb{FP}^{2}$ is indeed a homeomorphism on to its image, however I am struggling to understand how I can show the function and its inverse are continuous especially since were are dealing with ratios of points in the co-domain.