Question

Every finite set of point is​

Answer 1

Answer:

All finite sets in a T1 space are closed. Spaces like Rn are Hausdorff and therefore T1. But the Sierpinski space (which you suggest) is not a T1 space, and so not every finite set there is closed.

Note that if all finite sets were closed, universally, then every topology on a finite set would be the discrete topology. But then the trivial topology, {X,∅} wouldn't be a topology on any non-singleton finite set.

Answer 2

Answer:

the power set of a finite set is finite, with cardinality 2n. Any subset of a finite set is finite. The set of values of a function when applied to elements of a finite set is finite. All finite sets are countable, but not all countable sets are finite.

Explanation:

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