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Piece-wise closed functions and almost discretely σ-decomposable families

Part of: Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  26 February 2010

R. W. Hansell ,
J. E. Jayne  and
C. A. Rogers
R. W. Hansell
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268, U.S.A
J. E. Jayne
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WCIE 6BT
C. A. Rogers
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
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Extract

In [8,9] Jayne and Rogers studied piece-wise closed maps and ℱσ maps between metric spaces. A map f of a metric space X into a metric space Y is said to be an ℱσ map if: (a) f maps ℱσ-sets in X to ℱσ-sets in Y; and (b) f1 maps ℱσ-sets in Y back to ℱσ-sets in X. A map fof a metric space X into a metric space Y is said to be piece-wise closed if:it is possible to find a sequence X1, X2,… of closed sets in X, with with each setf(Xi), i ≥ 1, closed in Y, and with the restriction offto each Xi, a closed map (i.e., a continuous map that maps closed sets to closed sets).

MSC classification

Secondary: 54C50: Special sets defined by functions

Information

Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 229 - 247
Copyright
Copyright © University College London 1985

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