If the Universe Is Closed and Finite Then
Informally a finite set is a set which one could in principle count and finish counting. A closed curve is thus the image of a continuous mapping of a circle.
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The number of elements of a finite set is a natural number possibly zero and is called the cardinality or the cardinal number of the set.

. In mathematics particularly set theory a finite set is a set that has a finite number of elements. If the domain of a topological curve is a closed and bounded interval it is called a path also known as topological arc or just arc. There are two possible futures for our Universe continual expansion open and flat or turn-around and collapse closed.
Current values for the critical density range from 01 to 1 which produces a new dilemma from. The description of the various geometries of the Universe open closed flat also relate to their futures. Note that flat is the specific case of expansion to zero velocity.
A curve is simple if it is the image of an interval or a circle by an injective continuous function. For example is a finite set with five elements.
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