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Userspace refers to all pages beginning with a username, and connected with a particular user. They may be used for article drafts, tasks, jottings, or other purposes - e.g. User:Teratornis/Tasks is a list of tasks related to Appropedia, maintained by Teratornis. Normally an editor has free rein in their userspace, provided it is not used for spam or other activities likely to bring Appropedia, the Appropedia community or the Appropedia Foundation into disrepute.
These may be for joint use or for personal use.
These pages are still public, and anyone is able to edit them; however they are mainly the responsibility of the particular user. Unless there is an invitation to edit, use your discretion in editing. It is often best to restrict your editing to commenting. It is always acceptable to leave messages on the talk page, or the user's personal talk page. (The user's personal talk page is the place they are most likely to see a message, because of how notifications work in MediaWiki.
Instead of deleting an unsuitable article, an Appropedia admin may "userfy" the page, i.e. move the page to userspace, as a subpage of the userpage of the main editor. This allows the user to continue to work on it and/or move it to a more suitable site.