Theorem:-\ For aspace X, the F.A.E:\ (1)

x

is a

T_(2)

-space.\ let

y

be any point of

x

then for every

x!=y,EE

an open set

V

containing

y

s.t

x!i(n)/(b)ar (V)

\ (3) The diagonal set

\\\\Delta ={(x,x)/(x)inx}

is a closed subset in

x\\\\times x

.\ (4) and

U

is open

For a space X, the F.A.E: (1) X is a T2-space. (2) let y be any point of x then for every x=y, an open set v containing y s.t x/V (3) The diagonal set ={(x,x)/xX} is a closed subset in XX. (4) xX,{x}={U/xU and U is open } Question: a) prove it (3) (4) b) " " (4) (1)