An exemplary refill unit for a dispenser includes an inverted non-collapsing container for holding a liquid. A pump housing is secured to the bottom of the inverted non-collapsing container. The pump housing includes a pump chamber for pumping fluid out of the inverted non-collapsing container. The pump housing includes an annular venting chamber. The annular venting chamber has a floor with an opening therethrough. A vent valve is located within the venting chamber. The vent valve has a first wiper seal in contact with a wall of the annular venting chamber.
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