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We discuss the potential of a next generation space-borne Cosmic MicrowaveBackground (CMB) experiment for studies of extragalactic sources. Our analysishas particular bearing on the definition of the future space project, CORE,that has been submitted in response to ESA's call for a Medium-size missionopportunity as the successor of the Planck satellite. Even though the effectivetelescope size will be somewhat smaller than that of Planck, CORE will have aconsiderably better angular resolution at its highest frequencies, since, incontrast with Planck, it will be diffraction limited at all frequencies. Theimproved resolution implies a considerable decrease of the source confusion,i.e. substantially fainter detection limits. In particular, CORE will detectthousands of strongly lensed high-z galaxies distributed over the full sky. Theextreme brightness of these galaxies will make it possible to study them, viafollow-up observations, in extraordinary detail. Also, the CORE resolutionmatches the typical sizes of high-z galaxy proto-clusters much better than thePlanck resolution, resulting in a much higher detection efficiency; theseobjects will be caught in an evolutionary phase beyond the reach of surveys inother wavebands. Furthermore, CORE will provide unique information on theevolution of the star formation in virialized groups and clusters of galaxiesup to the highest possible redshifts. Finally, thanks to its very highsensitivity, CORE will detect the polarized emission of thousands of radiosources and, for the first time, of dusty galaxies, at mm and sub-mmwavelengths, respectively.

Exploring Cosmic Origins with CORE: Extragalactic sources in Cosmic Microwave Background maps