A check valve, comprising in combination: a housing having an inlet with a dome-shaped interior configuration and an outlet; an elastomeric dome-shaped valve element positioned entrained between said inlet and said outlet form a seal against said inlet, said elastomeric dome-shaped valve element having a plurality of cutouts that allow fluid flow therethrough thereby increasing the amount of fluid flow that may flow through the check valve when said elastomeric dome-shaped valve element is cracked open; said elastomeric dome-shaped valve element further comprises an integral annular skirt extending about its periphery; said plurality of cut-outs define a plurality of equally-spaced legs extending generally radially outward then downwardly to merge into said annular skirt; a width of said plurality of equally-spaced legs is defined by a width of said plurality of cut-outs to define said plurality of equally-spaced legs whose strength achieves a cracking pressure; an underside of said elastomeric dome-shaped valve element including a generally concave portion extending circularly annularly about said underside to define an outwardly extending point having a form of an upside-down three dimensional hyperbolic curve that precludes entrapment of air underneath said elastomeric dome-shaped valve element; said elastomeric dome-shaped valve element further comprising a central stem; said outlet comprising a dome-shaped interior configuration; said dome-shaped interior configuration of said inlet comprising an annular valve seat which forms a seal with an upper surface of said elastomeric dome-shaped valve element when said elastomeric dome-shaped valve element is in its at rest position within the housing; said dome-shaped interior configuration of said outlet comprising an annular seat on which said inwardly extending rim of said annular skirt is seated when said elastomeric dome-shaped valve element is in its at rest position; and a plurality of castellations having an inside diameter that is appreciably less than an outside diameter of said hyperbolic curve defined by said concave portion to limit inward travel of said elastomeric dome-shaped valve element as it is cracked open. a housing having an inlet with a dome-shaped interior configuration and an outlet; an elastomeric dome-shaped valve element positioned entrained between said inlet and said outlet form a seal against said inlet, said elastomeric dome-shaped valve element having a plurality of cutouts that allow fluid flow therethrough thereby increasing the amount of fluid flow that may flow through the check valve when said elastomeric dome-shaped valve element is cracked open; said elastomeric dome-shaped valve element further comprises an integral annular skirt extending about its periphery; said plurality of cut-outs define a plurality of equally-spaced legs extending generally radially outward then downwardly to merge into said annular skirt; a width of said plurality of equally-spaced legs is defined by a width of said plurality of cut-outs to define said plurality of equally-spaced legs whose strength achieves a cracking pressure; an underside of said elastomeric dome-shaped valve element including a generally concave portion extending circularly annularly about said underside to define an outwardly extending point having a form of an upside-down three dimensional hyperbolic curve that precludes entrapment of air underneath said elastomeric dome-shaped valve element; said elastomeric dome-shaped valve element further comprising a central stem; said outlet comprising a dome-shaped interior configuration; said dome-shaped interior configuration of said inlet comprising an annular valve seat which forms a seal with an upper surface of said elastomeric dome-shaped valve element when said elastomeric dome-shaped valve element is in its at rest position within the housing; said dome-shaped interior configuration of said outlet comprising an annular seat on which said inwardly extending rim of said annular skirt is seated when said elastomeric dome-shaped valve element is in its at rest position; and a plurality of castellations having an inside diameter that is appreciably less than an outside diameter of said hyperbolic curve defined by said concave portion to limit inward travel of said elastomeric dome-shaped valve element as it is cracked open.