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Jul 26, 2010 at 9:19 comment added Stefan Geschke Well. I think the fact that simple connectedness and being a subspace are two properties is just a notational issue. Moreover, if you consider an ambient space, what should be simply connected if not a subspace? Being a subfield of a field also means to be closed under various operations, and hence could be regarded as not just one property.
Jul 26, 2010 at 8:45 comment added Unknown Thanks, Dylan. But can you come up with two set having just one "big" property and not following the trend? In your case, though acceptable an answer, I get the feeling that simple-connectedness and being a subspace are two properties. See my comment above.
Jul 26, 2010 at 8:00 history answered Dylan Wilson CC BY-SA 2.5