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How to define inclusions in Mathematica?

Dear members of the Wolfram Community,
Does any one has define inclusions (set valued maps) such as
y=0 for x>0 and y=(-inf,0] for x=0, in Mathematica??
Thanks

Jesus Rico
POSTED BY: J Jesus Rico-Melgoza
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It's not really a function.  It has an infinite number of values of y for x = 0. 
I don't think Plot can handle that.
POSTED BY: Frank Kampas
y = Piecewise[{{0, x > 0}, {Interval[{-\[Infinity], 0}], x == 0}}]
POSTED BY: Frank Kampas
Thanks!
 I used your definition within a Plot function 
Plot[y, {x, -1, 1}, Exclusions -> None]
and get only a horizontal line that not correspond to expected function.

What am I doing wrong?

Jesus
POSTED BY: J Jesus Rico-Melgoza
Differential inclusions are very interesting generalizations of ordinary differential equations and definitions like the one you help me with are needed.

Thanks indeed!

Jesus 
POSTED BY: J Jesus Rico-Melgoza
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