CHAPTER XII - CONTINUOUS MAPPINGS

Abstract

This chapter focuses on continuous mappings. With the topological spaces X and Y and f: X → f is said to be continuous at the point x0 if , x0 ∈A ⇒ f(x)0 ∈ f(A for each A ⊂ X. Mappings continuous at each point are called, briefly continuous. The set of these mappings is denoted (YX)top, or briefly YX. The chapter also presents the proof of theorem that states that x0 ∈A ⇒ f(x)0 ∈ A ⇒ f(x) 0 ∈ f(A for each A ⊂ X is equivalent to x0 ∈ f-1(B) ⇒ f(x0) ∈ (B) for each B ⊂ Y.n.