(adsbygoogle = window.adsbygoogle || []).push({}); Unable to understand "Open Set"

I keep reading the definition of an open set & neighborhood, but I just don't seem to get it.

This is the defn - "a set U is open if any point x in U can be "moved" a small amount in any direction and still be in the set U."

I don't see how this condition can ever be satisfied.

For eg, after this, it typically says - "an open set is a solid region minus its boundary".

I don't understand this because a solid region minus the boundary does have a boundary. It's just that the new boundary is slightly smaller as compared to the previous boundary i.e. I am not able to grok the concept of how a point at the edge of a region can be moved outwards and still remain in the region.

Can someone explain this?

Same thing with understanding "Neighbourhood of a point" also?

Is there something else I need to study to understand this?

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# Unable to understand Open Set

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