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Definition: Suppose that T and T' are two topologies on a given set X. If T' includes T, we say that T' is finer than T; if T' properly contains T, we say that T' is strictly finer than T. Other terminology is sometimes used for this concept. If T' contains T, some mathematicians would say that T' is larger than T.
Source: Topology (second edition) by James R. Munkres