Let X be a topological space and an equivalence relation on X. Let X/ be the...

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Let X be a topological space and an equivalence relation on X. Let X/ be the quotient space and : XX/ the quotient map. 1. If the quotient space X/- is connected, is X connected? 2. Show that if (a) the quotient space X/ is connected and (b) for each point pe X/, the inverse image (p) is connected, then X is connected. Let X be a topological space and an equivalence relation on X. Let X/ be the quotient space and : XX/ the quotient map. 1. If the quotient space X/- is connected, is X connected? 2. Show that if (a) the quotient space X/ is connected and (b) for each point pe X/, the inverse image (p) is connected, then X is connected.