ABSTRACT
Let C ( X ; E ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2822.tif"/> denote the vector space of all continuous functions on a completely regular Hausdorff space X with values in a Hausdorff locally convex space E. Let C c ( X ; E ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2823.tif"/> denote the vector space C ( X ; E ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2824.tif"/> endowed with the topology of compact convergence. If K denotes the scalar field ( K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2825.tif"/> = ℝ or ℂ) then we write C ( X ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2826.tif"/> instead of C ( X ; K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072577/94f683e7-9f6e-41e2-9c5e-98432cdb82df/content/eq2827.tif"/> ).
