Ready-to-blossom bases in Chebyshev spaces

International audienceThis paper gives a survey on blossoms and Chebyshev spaces, with a number of new results and proofs. In particular, Extended Chebyshev spaces are characterised by the existence of a certain type of bases which are especially suited to enable us to prove both existence and properties of blossoms under the weakest possible differentiability assumptions. We also examine the case of piecewise spaces built from different Extended Chebyshev spaces and connection matrices