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... extension topology, defined as τ+(B)= { O ∪ (O’ ∩ B) / O,O’ ∈τ}, where B ∉ τ. By the definition of simple expansion we infer that all topologies are simple expansion topologies. Another significant contribution in the field of general topology was due to Levine[9]in 1970,who also introduced the noti ...
... extension topology, defined as τ+(B)= { O ∪ (O’ ∩ B) / O,O’ ∈τ}, where B ∉ τ. By the definition of simple expansion we infer that all topologies are simple expansion topologies. Another significant contribution in the field of general topology was due to Levine[9]in 1970,who also introduced the noti ...
Semi-continuity and weak
... By Lemma L4 and the previous five examples, we obtain the following diagram, where Л -+-> J5 means that Ä does not necessarily imply B. O.W. ...
... By Lemma L4 and the previous five examples, we obtain the following diagram, where Л -+-> J5 means that Ä does not necessarily imply B. O.W. ...
Modal logics based on the derivative operation in topological spaces
... For A ⊆ X , a point x ∈ X is a co-limit point of A iff there exists an open neighborhood B of x such that B ⊆ A ∪ {x} For A ⊆ X , t(A) is the set of co-limit points of A Remind that In(A) = A ∩ t(A) For A ⊆ X , a point x ∈ X is a limit point of A iff for all open neighborhoods B of x, A ∩ (B \ {x}) ...
... For A ⊆ X , a point x ∈ X is a co-limit point of A iff there exists an open neighborhood B of x such that B ⊆ A ∪ {x} For A ⊆ X , t(A) is the set of co-limit points of A Remind that In(A) = A ∩ t(A) For A ⊆ X , a point x ∈ X is a limit point of A iff for all open neighborhoods B of x, A ∩ (B \ {x}) ...
The derived category of sheaves and the Poincare-Verdier duality
... for bounded complexes, for complexes bounded from below and for complexes bounded from above. Using the same procedure as above we obtain derived categories Q : K pAq Ñ D pAq satisfying similar universality properties. We deduce that there exist natural injective functors i : D pA q Ñ D p ...
... for bounded complexes, for complexes bounded from below and for complexes bounded from above. Using the same procedure as above we obtain derived categories Q : K pAq Ñ D pAq satisfying similar universality properties. We deduce that there exist natural injective functors i : D pA q Ñ D p ...
