Remark 3
Tag 09R7, permanent. Cite it as [Bourbaki, Tag 09R7].
Integration, IX, p. 60, § 5. Measures on completely regular spaces
If T is completely regular, the mapping of T into is a homeomorphism (GT, IX, §1, No. 5).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.