Topology List
It seems to me a wise idea to create a list of terms and important theorems
that we have at our disposal. I will try to update the list of terms
that we have defined. I recommend each of you creating a reference
place
where you write the definition of each of these terms and state the relevant
theorems.
Terms
topology, topological space, open set
closed set
T1/2 space
T1 space
T2 space (Hausdorff space)
T3 space (regular space)
T4 space (normal space)
closure (2 definitions)
interior (2 definitions)
boundary (2 definitions)
continuous function
homeomorphism (homeomorphic spaces)
subspace, subspace topology
basis for a topology
product topology
identification / quotient map / quotient function
identification space / quotient space
connected / disconnected
connected component
path connected
compact
manifold
surface
Theorems
Write down every theorem you can find that we have proven. You never
know when you might need it. It's handy to have a list of results for
your reference.