Glasnik Matematicki, Vol. 33, No.1 (1998), 115-121.

MAPPINGS ON WEAKLY ARCWISE OPEN DENDROIDS

Isabel Puga

Abstract.   A dendroid X is said to be weakly arcwise open (WAO) at p ∈ X if each arc component of X \ {p} is either open or has empty interior. Thew dendroid X is WAO if it is WAO at p for each p ∈ X. This paper deals with mappings which preserve the WAO property. In particular, we prove that the WAO property is preserved by monotone mappings on dendroids and by locally monotone mappings on fans.

1991 Mathematics Subject Classification.   54F50, 54E40.

Key words and phrases.   Dendroid, fan, arc-component, weakly arcwise open (WAO) property, Kelley's property, monotone, locally monotone, quasi-monotone and confluent mappings.