Prove that continuous function of a continuous function is continuous.

Let f:X→Yf: X \to Y and g:Y→Zg: Y \to Z be two continuous functions, where X,Y,ZX, Y, Z are topological spaces. We want to show that the composition g∘f:X→Zg ___ ___ ________ ___ _________ _____ __________ ________ _________ ____.
__________ _____ _________ ______ __________ ________ ___ ______ ___ _________ _______ __________.
________ ____ _______ _________ ______ ____ ________ ____ ________ ___ ______.
_______ ____ ____ ___ _____.
__________ ______ _____ _________ ___ _____ ______.
_________ _________ _________ _____ _____ _______ ______ ___ __________ ____ ______ ________.
__________ ______ _____ __________ _____ ____ ___.
________ ___ __________ _______ _________ __________.
_______ ________ __________ ____ __________ ___ ______.
_____ ________ _________ ____ _________ __________ ____ _____ __________ ________ __________.
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