De Morgan’s Laws (*)
Property of the double complement (H)
Uniqueness theorem for the maximum/minimum of a set (H)
Characterization theorem for the supremum/infimum of a set, using left/right neighborhoods (H)
Triangle inequality for the norm (H)
All neighborhoods are open sets (*)
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A set is open if and only if its complement set is closed (H)
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A monotone function is invertible if and only if it is strictly monotone (*)
Preservation of maximizers/minimizers with respect to strictly increasing composition (*)
Fenchel’s theorem: local-global maximum (minimum) property for concave (convex) functions (*)
Concave (convex) functions have convex upper (lower) contour sets (*)
Concave (convex) functions are quasi-concave (quasi-convex) (H).
For an eventually strictly positive sequence xn, xn tends to +infinity if and only if 1/xn tends to zero (*)
Theorem on the uniqueness of the limit for sequences (* only in the case of finite limits)
Boundedness theorem for convergent sequences (H)
Regularity theorem for monotone sequences (*)
Limit of a sum of sequences (* only in the case of finite limits)
Comparison criterion for sequences (*)
Theorem on the characterization of xn ~ yn with the use of o (H)
Behavior of the geometric series (*)
Behavior of the Mengoli series (H)
Necessary condition for the convergence of a series (H)
Regularity theorem for series with positive terms (H)
Theorem on the uniqueness of the limit for functions (H only in the case of finite limits)
