A connector comprising: a housing having a flow path through which a liquid passes, and a substantially circular pipe connecting port which communicates with the flow path; and a valve (3; 43; 53) formed of an elastic material and adapted to block the pipe connecting port of the housing, wherein the valve comprises: a columnar deformable portion having a top surface exposed from the pipe connecting port, a bottom surface opposite to the top surface, and a slit (33; 45; 55) extending from the top surface to the bottom surface; and a ring-shaped fixing piece protruding from an outer peripheral surface of the deformable portion, in an intermediate portion between the top surface and the bottom surface, and fixed to the housing, wherein when the top surface is pressed by a pipe, the deformable portion will be displaced toward the flow path while elastically deforming, so that inner surfaces which define the slit face, the flow path of the housing, and the top surface form an opening which communicates with the flow path, characterized in that the housing comprises a curved surface configured to guide the elastic deformation of the valve so that at least a portion of the bottom surface of the deformable portion rolls back toward a lateral outer side, and in that the pipe connecting port includes a first member and a second member, wherein the first member includes a tubular portion and a flange portion; the fixing piece of the valve (3; 43; 55) abuts one end face of the tubular portion in an axial direction; and the curved surface is formed on an inner surface of the tubular portion, wherein the inner diameter of the curved surface becomes larger as it goes toward the other end. a housing having a flow path through which a liquid passes, and a substantially circular pipe connecting port which communicates with the flow path; and a valve (3; 43; 53) formed of an elastic material and adapted to block the pipe connecting port of the housing, wherein the valve comprises: a columnar deformable portion having a top surface exposed from the pipe connecting port, a bottom surface opposite to the top surface, and a slit (33; 45; 55) extending from the top surface to the bottom surface; and a ring-shaped fixing piece protruding from an outer peripheral surface of the deformable portion, in an intermediate portion between the top surface and the bottom surface, and fixed to the housing, a columnar deformable portion having a top surface exposed from the pipe connecting port, a bottom surface opposite to the top surface, and a slit (33; 45; 55) extending from the top surface to the bottom surface; and a ring-shaped fixing piece protruding from an outer peripheral surface of the deformable portion, in an intermediate portion between the top surface and the bottom surface, and fixed to the housing, wherein when the top surface is pressed by a pipe, the deformable portion will be displaced toward the flow path while elastically deforming, so that inner surfaces which define the slit face, the flow path of the housing, and the top surface form an opening which communicates with the flow path, characterized in that the housing comprises a curved surface configured to guide the elastic deformation of the valve so that at least a portion of the bottom surface of the deformable portion rolls back toward a lateral outer side, and in that the pipe connecting port includes a first member and a second member, wherein the first member includes a tubular portion and a flange portion; the fixing piece of the valve (3; 43; 55) abuts one end face of the tubular portion in an axial direction; and the curved surface is formed on an inner surface of the tubular portion, wherein the inner diameter of the curved surface becomes larger as it goes toward the other end. the first member includes a tubular portion and a flange portion; the fixing piece of the valve (3; 43; 55) abuts one end face of the tubular portion in an axial direction; and the curved surface is formed on an inner surface of the tubular portion, wherein the inner diameter of the curved surface becomes larger as it goes toward the other end.