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Two pathological countable topological spaces are constructed. Each is quasimetrizable and has a simple explicit quasimetric. One is a locally connected Hausdorff space and is an extension of the rationals. The other is a connected space which becomes totally disconnected upon the removal of a single point. This space satisfies the Urysohn separation property-a property between Tí and T¡-and is an extension of the space of rational points in the plane. Both are one dimensional in thedoi:10.1090/s0002-9939-1970-0263005-0 fatcat:rxpuro57yrafjl2z6c5m4ioiyi