Domain of a Function | Open or Closed Interval?

Thread starter Niles
Start date Dec 12, 2009
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Domain Function

AI Thread Summary

A function defined at a single point, such as f(x) = 2, is considered to be defined on a closed interval. The reasoning is that a single point can be represented as a closed interval, such as [a, a], where 'a' is the point. However, the classification can vary based on the topology applied to the real numbers. In standard topology, single points are closed sets, reinforcing the closed interval classification. Ultimately, the determination of open or closed intervals can depend on the specific topological context.

Dec 12, 2009

Niles

Homework Statement

Hi

If I have a function defined in one point only given by e.g.

f(x) = 2,

then is the function f defined on a open "interval" or a closed "interval"?

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Dec 12, 2009

CompuChip

Science Advisor

Homework Helper

Simple answer: a single point is a closed interval.

Complicated answer: it depends on the topology you put on R.

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