Topology, I think it is the top course in the field of Algebra. “Top” not only means that it can be widely used in many aspects, including the finance, the computer network, etc but is really hard to learn and understand because it is too abstract.

But it does not matter that topology is an interesting course. For example, topology space is always called “Plasticine Space” which means it can be stretched and reshaped to any other “shapes” with the properties never changed. Just like the plasticine which we played in the early ages.

The key to comprehend topology is remembering the defines well. Also, understanding them is also important. Only if you can repeat these defines without thinking and understand what it is can you get to master some really hard theories without obstacles.

It may be a hard time to remember all the defines because the defines in the latter part always rely on the fore ones. And it will spend a really long time to achieve the level of recalling a define when you hear the name.

So, here is a summary of various defines in topology. This would be useful to remember them and hope this will be useful for your revision.

By away, as for the theories of topology, the handout we used is written by a really excellent professor and I am not sure can I upload his handout here. So, please reference the textbook more and master the theories there.

Link：https://github.com/cbhua/note-math/tree/master/Topology