A note on the Fell-continuous selections;

In this paper,on the base of the property for the selection of set-valued mapping,we introduce a relation of almost lower semicontinuous and continuous selection for metric projection in Banach space.

We discusses the existence of continuous selections of fixed points for contractive set_valued mappings in Sobolev space, establishes a continuous selection theorem similar to Michael s,and proves that any two continuous selections can be joined by a homotopy, and constructs a class of absolute contractive sets in Sobolev space.

This paper presents an extended form of approach to continuous selections of arbitary images of values of sets and proves the existence of the extended form of approach to continuous selctions.

We characterize the countable paracompactness of normal spaces by the existence of continuous selections for l s c closed convex set valued mappings on locally convex Fréchet spaces An extensor class including separable Banach spaces of countable paracompactness is give

This paper gives a charactering theorem of such T 0 space with χ(x)≤m by using Mrowkas m almost metric space, which extended a similar famous theorem of ponomave¨v who used the ordinary metric space and continuous open mapping of such space.