For the Sugar-free Quick Pickled Red Onions:

1. Whisk the vinegar, water, allulose and salt together in a medium saucepan and bring to a boil over high heat.   Cook, whisking frequently, until sweetener and salt dissolve, 2 to 3 minutes.
2. Meanwhile, transfer onions to large jar or bowl. Pour hot pickling liquid over onions and let cool for 20 minutes. Cover and refrigerate until onions turn pink and are seasoned throughout, at least 8 hours.
3. Onions can be refrigerated in pickling liquid for up to 2 weeks.

For the Sugar-free Canned Pickled Red Onions:

1. Prepare 4 - 16 oz wide mouth mason jars - Bring a extra large canning pot filled with water to a boil.  Place the lids and the jars in the water and allow them to simmer to sterilize while you prepare the onions.
2. Thinly slice the onions and set aside.
3. In a medium-size saucepan, combine the vinegar, allulose and salt and bring to a boil, simmer until allulose and salt have dissolved, about 3-5 minutes.
4. Remove the lids and the jars from the water bath and place them on a kitchen towel.  Be careful as they are really hot.
5. Once jars have cooled and can be handeled,  add 1 teaspoon of pickling spices to the bottom of each mason jar.  Stuff (and I mean REALLY stuff!) the sliced onions into each jar.
6. Using a funnel, carefully pour the bine over the onion filled jars, leaving 1/4 inch of space at the top. Add the lids and tightly seal the jars with the lids to "finger tightness". (If any liquid falls around rim of jar, use a paper towel to clean the rim.)
7.  To process, make sure that your rack is on the bottom of the canner and place the jars in the water bath, using the jar handle tool to lower the jar into the bath, making sure that the water covers each of the jars by 1 to 2 inches. Add hot water to the canner if it doesn't measure up.
8. Allow the water to return to a boil.  Once the water has come to a boil, start your timer for 10 minutes.
9. When complete, turn off the heat and carefully, using jar handler tongs, remove the jars.  Place the jars on a dishtowel and allow to cool to room temperature.
10. As the jars cool, you will hear a "popping" noise, meaning that the glass has cooled and the lids have sealed shut.  Be patient as this can take several hours and even may take overnight.
11. If any jars do not seal, place those jars in the fridge and use within one month.  All sealed jars can be stored at room temperature for up to 1 year.