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In this paper, we will present several necessary and sufficient conditions on a commutative ring such that the algebraic and geometric local cohomologies are equivalent.
It is well-known that the concentric circle space has no -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.
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