Which of the intervals (-3, 3), [4, 7], (-4, 5], (0,) and [0,
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Examples 5.1.2(a): |
Which of the intervals (-3, 3), [4, 7], (-4, 5], (0, |
= min( 3 + x, 3 - x ).
Then > 0,
and the interval
(x - / 2,
x + / 2)
is contained in (-3, 3). In fact, the same argument works for any
interval of the form (a, b) with a, b real numbers.
, 4) and
(7, ).
, -4] and
(5, ) is not
open at x = -4.
) and also the
interval
(- , 0) are both open,
because every point in the set contains a neighborhood contained
inside the set.
)
and also the interval
(- ,0] are both
closed, because their complements are the open sets mentioned above.