Types of Multivalued Functions
One can differentiate many continuity concepts, primarily closed graph property and upper and lower hemicontinuity. (One should be warned that often the terms upper and lower semicontinuous are used instead of upper and lower hemicontinuous reserved for the case of weak topology in domain; yet we arrive at the collision with the reserved names for upper and lower semicontinuous real-valued function). There exist also various definitions for measurability of multifunction.
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“The wider the range of possibilities we offer children, the more intense will be their motivations and the richer their experiences. We must widen the range of topics and goals, the types of situations we offer and their degree of structure, the kinds and combinations of resources and materials, and the possible interactions with things, peers, and adults.”
—Loris Malaguzzi (1920–1994)
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