Continuity/R and C/Addition and multiplication/Fact/Proof/Exercise

Show that the addition

${\mathbb {K} }\times {\mathbb {K} }\longrightarrow {\mathbb {K} },(x,y)\longmapsto x+y,$

and the multiplication

${\mathbb {K} }\times {\mathbb {K} }\longrightarrow {\mathbb {K} },(x,y)\longmapsto x\cdot y,$

are continuous.

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