A STRONG COMPLETENESS CONDITION IN UNIFORM SPACES WITH WELL ORDERED BASES
A natural strengthening of the completeness hypothesis, called -completeness, allows us to extend to ! -metric spaces some properties of complete metric spaces which fail to hold if only the completeness condi- tion is assumed. In this way we achieve some results on hyperspace theory, dealing with supercompleteness and with selections of multivalued functions. The notion of -completeness is investigated and it is proved that quite important classes of ! -metric spaces have this property.
A Result about Selectors in non-Archimedean Spaces
Summary. - A sort of strong completeness property for subsets of a non-Archimedean space is defined. On the subsets which satisfy this property there exists a Vietoris continuous selector. The set of discrete closed subsets of R has a continuous selector when it is equipped with the Vietoris topology induced by the Michael line. Some properties of the tree of a non-Archimedean space are used. 1. Preliminaries
Avocado Flowering 1
The avocado (Persea americana Mill.) has increased in importance over the years in many countries around the world. The United States, Mexico and Brazil lead in world commercial production, while Israel, South Africa, Australia, New Zealand, the Philippines, Spain, Cyprus, Canary Islands, Chile, Ecuador, Venezuela, Greece, and the Caribbean area are actively increasing commercial production (B.O. Bergh, personal communication; Gustafson 1976). The history of the avocado has been detailed by Gustafson (1973, 1975,1976) and others (Bergh 1975b, Knight 1980; Popenoe 1924; Ruehle 1958; Schroeder 1958; Williams 1976). Several reviews have been published on various aspects of the avocado, including its botany (Knight 1980; Purseglove 1968; Williams 1976), breeding (Bergh 1975b), horticulture (Hodgson 1930b; Ruehle 1958; Ryerson et al. 1924), cultivars (Campbell and Malo 1976), and pollination (Gustafson and Bergh 1966). A recent collection of papers discussing the horticultural aspects of avocado production is found in Sauls et al. (1976).