Topology : Topological Spaces

Study concepts, example questions & explanations for Topology

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Example Questions

Example Question #1 : Topological Spaces

Determine whether the statement is true or false:

The Betti number of an object gives the number of holes in each dimension in a given topological space.

Possible Answers:

True

False

Correct answer:

True

Explanation:

In topology, Betti numbers represent the various dimensions of a topological space in regards to the number of holes that are present. There are four different simplices depending on the dimension: zero, one, two, three.

These are also referred to as:

Zero simplex refers to a point or vertex.

One simplex refers to a line or edge (which is connected by two points)

Two simplex refers to a face (which is connected by three lines)

Three simplex refers to the 3D object created by two faces.

Therefore by definition the statement,

"The Betti number of an object gives the number of holes in each dimension in a given topological space." is true. 

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