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Approximative compactness and continuity of metric projections: Corrigendum

Published online by Cambridge University Press:  17 April 2009

B.B. Panda  and
O.P. Kapoor
B.B. Panda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India
O.P. Kapoor
Affiliation:
Department of Mathematics, Indian Institute of Technology - Kanpur, Kanpur, India., India
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There is a small error in the proof of Lemma 1 [1], namely, that there may not be a subsequence of the sequence {Φn} converging to Φ in the weak*-topology. Thus equation (5) should read: In view of continuity of Pk we have

The same error occurs in the proof of Theorem 1 and Lemma 2 also. Therefore, equation (7) should read

and this leads to lim . Similarly, equation (8) should read

which implies that Ψn (x) → ‖x‖. Then there is no need of taking a subsequence.

All the same the results are not affected by the above error.

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 319 - 320
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Panda, B.B. and Kapoor, O.P., “Approximative compactness and continuity of metric projections”, Bull. Austral. Math. Sac. 11 (1974), 47–55.CrossRefGoogle Scholar