engleski

A note on light inducued mappings

Let a mapping f : X ! Y between continua X and Y be given. We shall prove: a) if the induced mapping 2f : 2X ! 2Y is light, then w(X) = w(Y ). In particular, if Y is metrizable, then X is metrizable, b) if the induced mapping C(f) : C(X) ! C(Y ) is light and X is a D-continuum, then w(X) = w(Y ).

Continuum; induced mapping; light mapping

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