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#{{em|{{visible anchor|Real homogeneity|Real homogeneous}}}}: <math>f(rx) = r f(x)</math> for all <math>x \in X</math> and all real <math>r.</math>
#* This property is used in the definition of a {{em|real}} [[linear functional]].
#{{em|{{visible anchor|Homogeneity|Homogeneous}}}}:{{sfn|Kubrusly|2011|p=55}} <math>f(sx) = s f(x)</math> for all <math>x \in X</math> and all scalars <math>s \in \mathbb{F}.</math>
#* It is emphasized that this definition depends on the scalar field <math>\mathbb{F}</math> underlying the ___domain <math>X.</math>
#* This property is used in the definition of [[linear functional]]s and [[linear map]]s.
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