anyone can help with this:
Let $X$ be the so-called Hawaiian Earrings, i.e. union of these circles:
$$\left(x − \frac1n\right)^2 + y^2 = \left(\frac1n\right)^2 , n = 1, 2, \dots\;,$$
with the induced topology of the plane and let $Y$ be the space when we identify every integer points of real line to a point. Show that $X$ and $Y$ are not homeomorphic.