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Subbase
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<p>In <a href="/facts/Topology/2EqW47cU">topology</a>, a subbase (or subbasis, prebase, prebasis) for the <a href="/facts/Topology_(structure)/v2ut7CbK">topology</a> τ of a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> (<i>X</i>, τ) is a subcollection B {\displaystyle B} of τ {\displaystyle \tau } that generates τ , {\displaystyle \tau ,} in the sense that τ {\displaystyle \tau } is the smallest topology containing B {\displaystyle B} as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below. </p><p>Subbase is a weaker notion than that of a <a href="/facts/Base_(topology)/8EDSDVPD">base</a> for a topology. </p>