In this article we introduce a topological analogue of measure of noncornpact-ness. We show some basic properties of that kind of measure. We show by counter-examples, why it is necessary to consider the system of all open coverings and not only a special kind of coverings like balls coverings in metric spaces. We apply the measure of noncompactness to prove upper semicontinuity of the limit of decreasing net of upper semicontinuous multifunctions.
展开▼
