Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: f – 1(Y) = X

Topology Sets and Functions (XXVIII) Functions Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: f – 1(Y) = X See the attached file.

Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: B1 is a subset of B2 implies f – 1(B1) is a subset of f – 1(B2).

Topology Sets and Functions (XXIX) Functions Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: B1 is a subset of B2 implies f – 1(B1) is a subset of f – 1(B2). See the attached file.

Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f – 1 (Ui Bi) = Ui f – 1 (Bi)

Topology Sets and Functions (XXX) Functions Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f – 1 (Ui Bi) = Ui f – 1 (Bi) See the attached file.

Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f– 1 (∩i Bi) = ∩i f– 1 (Bi)

Topology Sets and Functions (XXXI) Functions Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f– 1 (∩i Bi) = ∩i f– 1 (Bi) See the attached file.

Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f– 1 (B') = f– 1 (B)'

Topology Sets and Functions (XXXII) Functions Consider an arbitrary mapping f : X → Y. Prove the main property of the second set mapping: f– 1 (B') = f– 1 (B)' See the attached file.