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    Composition, products, and corestrictions of open maps

    P-UNL871F13-PS5.2

    Area
    Topology
    Topics
    Continuity, Product Topology
    Status
    draft
    Contents

    1. Show that a composition of open maps is open.

    2. Show that a finite product of open maps is open. Determine whether the corresponding assertion is true for an infinite product.

    3. Suppose \(f:X\to Y\) is open and \(f(X)\subseteq B\subseteq Y\). Show that the corestriction \[ f^B:X\to B \] is open when \(B\) has the subspace topology.

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