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    Proofs that an Inclusion Map is Continuous

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    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.

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    is the set of all real numbers. For any , we define and . As an order topology, and are base open sets and any open set in is the finite intersections of the base open sets.
    To show that inclusion map is continuous, we need to prove that ...

    Solution Summary

    This provides an example of proving the continuity of an inclusion map.