Abstract
A new class of multifunctions, called upper (lower) -continuous multifunctions, has been defined and studied. Some characterizations and several properties concerning upper (lower) -continuous multifunctions are obtained. The relationships between upper (lower) -continuous multifunctions and some known concepts are also discussed.
Highlights
General topology has shown its fruitfulness in both the pure and applied directions. In reality it is used in data mining, computational topology for geometric design and molecular design, computer-aided design, computer-aided geometric design, digital topology, information system, and noncommutative geometry and its application to particle physics
One can observe the influence made in these realms of applied research by general topological spaces, properties, and structures
Continuity is a basic concept for the study of general topological spaces
Summary
General topology has shown its fruitfulness in both the pure and applied directions. In reality it is used in data mining, computational topology for geometric design and molecular design, computer-aided design, computer-aided geometric design, digital topology, information system, and noncommutative geometry and its application to particle physics. A subset A of a generalized topological space X, μX is said to be μX-α-regular if, for each point x ∈ A and each μX-open set U of X containing x, there exists a μX-open set G of X such that x ∈ G ⊆ cμX G ⊆ U.
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