Open mappings increasing order

Charatonik, Janusz; Charatonik, Włodzimierz

doi:10.1090/S0002-9939-97-04096-3

Open mappings increasing order
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by Janusz J. Charatonik and Włodzimierz J. Charatonik

Proc. Amer. Math. Soc. 125 (1997), 3725-3733

DOI: https://doi.org/10.1090/S0002-9939-97-04096-3

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Abstract:

It is shown that an analog of Whyburn’s theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.

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