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- Jun 20, 2014

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Call an

__$S$-space over a topological space $B$__a pair $(E,p)$ where $E$ is a topological space and $p$ is a local homeomorphism from $E$ into $B$. A

__morphism of $S$-spaces__$(E_1,p_1)$, $(E_2,p_2)$ over $B$ is a continuous mapping $\phi : E_1 \to E_2$ such that $p_1 = p_2 \circ \phi$. Show that if $\phi$ is a morphism of $S$-spaces, then $\phi$ is a local homeomorphism if and only if $\phi$ is an open mapping.

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