The Tokyo Subway reference article from the English Wikipedia on 24-Apr-2004
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Tokyo Subway

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The Tokyo Subway is one of the world's most extensive subway networks. The two primary subway operators are:

Several other railways in the capital, notably the Tokyo Waterfront Railway, also qualify as subways by most definitions.

On April 1, 2004, the Teito Rapid Transit Authority was privatized and renamed the Tokyo Subway Co. Ltd (東京地下鉄株式会社, Tōkyō Chikatetsu K.K.). The company will also use the name Tokyo Metro (東京メトロ) for promotional purposes.

The privatization affects only the TRTA, and Toei will continue to operate its own lines separately.