Vented non-collapsing containers, refillable refill containers, dispensers and refill units

Exemplary embodiments of dispensers and refill units are disclosed herein. An exemplary refill unit for a soap, sanitizer or lotion includes a non-collapsing container. The non-collapsing container includes a neck. An annular projection is located at least partially on the neck. A one-way valve is located proximate the annular projection. The one-way valve allows air to flow into the non-collapsing container once the vacuum pressure in the container reaches the cracking pressure of the one-way valve and the one-way valve prevents liquid from flowing out of the annular projection. In addition, a pump for pumping the contents of the container out of the container is also included.