An apparatus for mapping and/or ablating tissue includes a braided conductive member that that may be inverted to provide a ring-shaped surface. When a distal tip of the braided conductive member is retracted within the braided conductive member, the lack of a protrusion allows the ring-shaped surface to contact a tissue wall such as a cardiac wall. In an undeployed configuration, the braided conductive member is longitudinally extended, and in a deployed configuration, the distal end of the braided conductive member is retracted to invert the braided conductive member.