Chain (algebraic topology)
A chain in algebraic topology is like a bunch of toys that we can put together in a line. Each toy is called a "simplex". There can be different types of simplexes like points, lines, triangles, and more.
We can put these simplexes together in a line like a string of beads. We call this line a "chain". Think of it like a necklace we make with different colored beads. Each bead is like a simplex and the necklace is like a chain.
We can do different things with chains, like adding them together or multiplying them. This helps us understand how they are connected to each other. We can also break chains into pieces, like taking off a bead from the necklace.
By studying chains and how they are connected, we can learn more about the spaces they are in. It's kind of like how we learn more about a story by looking at how the different parts fit together.
Algebraic topology is all about studying the shapes and spaces by using things like chains and simplexes. By understanding chains better, we can understand the shapes and spaces better too.
We can put these simplexes together in a line like a string of beads. We call this line a "chain". Think of it like a necklace we make with different colored beads. Each bead is like a simplex and the necklace is like a chain.
We can do different things with chains, like adding them together or multiplying them. This helps us understand how they are connected to each other. We can also break chains into pieces, like taking off a bead from the necklace.
By studying chains and how they are connected, we can learn more about the spaces they are in. It's kind of like how we learn more about a story by looking at how the different parts fit together.
Algebraic topology is all about studying the shapes and spaces by using things like chains and simplexes. By understanding chains better, we can understand the shapes and spaces better too.