The variable X-ray sky requires wide-field monitoring with high sensitivity. We refer on novel X-ray telescopes with high sensitivity as well as large field of view. The results are very promising, allowing the proposals for space projects with very wide-field Lobster-eye X-ray optics to be considered. The novel telescopes will monitor the sky with unprecedented sensitivity and angular resolution of order of 1 arcmin. They are expected to contribute essentialy to study and to understand various astrophysical objects such as AGN, SNe, GRBs, X-ray flashes, galactic binary sources, stars, CVs, X-ray novae, various transient sources, etc.
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