I don't know if singlet is an Aussie word. We use it in Canada but usually only to refer to a sleevless top that is used for athletics, especially running. Maybe it's more of a proper English word as opposed to an American English word. sort of like colour verses color, behaviour/behavior.
Oh, in the US, they call a sleeveless cotton Tee, like the kind you wear under a dress shirt, a "wife-beater"![]()
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, because that's what lower class men will sometimes wear when it's hot, (without anything over it), usually while dirnking beer outside of a shack of some sort.
I know, it's a nasty term but somehow it brings the right picture to mind.