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question 1.doc
be the map defined by
.
Continuity of a map is investigated. The solution is detailed and well presented.
Topological Spaces : Continuity of Map - Let X and Y be topological spaces. Show that, if Y has the indiscrete topology, then any map f: X--> Y is continuous.
Trivial Topology, Continuity and Connectedness - Let X and Y be topological spaces, where the only open sets of Y are the empty set and Y itself, i.e., Y has the trivial topology.
• Show that any map X --> Y is continuous
• Show that Y is path ...
Inclusion map - Show that the inclusion map i:Q -> R defined by i(q)=q for all q in Q, is continuous where both Q (rational numbers) and R(real numbers) are given the order topology.