Could someone please enlighten me if my valve is broken? I think this is a Dunlop valve but the core seems completely stuck to the cap. No matter how much I twist and turn the core always comes off and the tire deflates. There is nothing inside the tube in the picture, it leads directly inside the tire. I can inflate the tire when the core is off but then there is no way to reattach is fast enough because there is literally nothing stopping the air. Thank you in advance!
If you can't get the black plastic cap off of the valve core, you'll need to replace the core. I would take a couple pair of pliers and secure one around the textured part of the core and use the other pair to try and twist off the black cap. Alternatively, you can use a Dremel type rotary tool with a cut blade and score a line through the black plastic cap. You may saw two lines on opposite sides of the cap to improve the releasing of the black cap. In any case, that black plastic cap must come off the core in order for the core to be of any use. Removing the black cap will not affect the air tightness of the system as that is accomplished by a ball bearing or spring loaded rubber within the core itself. It is indeed a Dunlop valve with a modern core you are dealing with. Wikipedia article on Dunlop valve