## Continuous selections for metric projections and interpolating subspaces |

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### Contents

Invariance of Regular Weakly Interpolating Subspaces | 19 |

Semidefinite Property of Regular Weakly Interpolating Subspaces | 37 |

Local Alternation Elements | 63 |

Copyright | |

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alternation element alternation signature ofG Approx approximation theory assume Brosowski C Z(g card(A card(bdZ(g card(supp card(Z(g change signs Chebyshev alternation phenomena completes the proof continuous function continuous metric selections continuous selection contradicts Corollary 4.2 Cq(T Definition 7.2 Deutsch dimG dimG(intZ(g dimG(T dimG|,upp dimG|x dimGU element of f\x exist a subnet exist neighborhoods existence of continuous extremal signature ofG f from G finite-dimensional subspace G Co(T g G G G satisfies NS(0 G supp G V(T G(intZ(g implies intZ(g intZ(G(A Lemma Let g Lipschitz continuous locally connected lower semicontinuity Math metric projections Niirnberger and Sommer nonempty Nurnberger open set primitive extremal signature proved quasi-Haar subspace regular weakly interpolating selections for metric semidefinite sign changes signature of G spline functions strict best approximation Strong uniqueness supp aa Suppose that G Theorem 4.2 weak Chebyshev subspace weakly interpolating subspace Z-subspace zero interval zeros with sign