Medical apparatus for use in the treatment of breathing or respiratory disorders, respiratory sleep disorders, snoring and parts therefor, namely, air pressure generator, air pressure controller, air capacitors, textile headgear specially adapted for use with medical ventilator mask interfaces, nasal pillows, nasal ventilation interface, and tubing; medical apparatus, namely, automatic positive airway pressure (APAP) devices and parts therefor; medical apparatus, namely, continuous positive airway pressure (CPAP) devices and parts therefore; medical apparatus, namely, positive end-expiratory pressure (PEEP) devices and parts therefor; Textile headgear specially adapted for use with medical respiratory masks and parts therefore; medical apparatus and instruments for monitoring respiratory events that transmit data about those respiratory events through the internet, and parts therefore