Question

can any one tell me how an empty set is an open set?

Answer 1

what is the complament of the empty set?

Answer 2

universal set. but what's its relation with complement of the empty set?

Answer 3

one easy way to see that the empty set is open is to notice that the universal set is closed...and the complement of a closed set is open.

Answer 4

ok but can u explain that u recognised that universal set is closed?

Answer 5

it contains all its limit points

Answer 6

can u give me some examples relating to open and closed sets in order to clear my concept.

Answer 7

on the real line (0,1) is open

[0,1] is closed

(0,1] is not open or closed

Answer 8

set {1,2,3......} is open or closed?

Answer 9

are you using the reals as your universal set?

Answer 10

does this metter that whether i am taking real or not?

Answer 11

yes

Answer 12

how?

Answer 13

suppose you have the set \(A=\{1\}\)

if \[U=\{1\}\] then \(A\) is both open and closed

if \[U=\mathbb{R}\]

then \(A\) is only closed. It is not open.

Answer 14

{1,2,3......} is neither open nor closed right?

Answer 15

it is atleast closed...but it depends on what your universal set is to get the full answer

Answer 16

how can u say if U={1}
then A is both open and closed. i think it is closed.

Answer 17

it is closed, but it is also open

Answer 18

set can be open and closed at the same time...that are call clopen sets

Answer 19

{1,2,3......} is my universal set

Answer 20

then it is both open and closed

Answer 21

shouldn't it [1,infinity)? then how both?

Answer 22

I don't follow...how can you have \([1,\infty)\)

if your universal set is \(\{1,2,3,\ldots\}\)

Answer 23

ok leave it. thanks for answering my questions