9/13 meeting
# some reference
https://math.ucr.edu/~res/math205B-2018/Munkres%20-%20Topology.pdf
https://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf
https://math.ntnu.edu.tw/~li/Topology/Topology.pdf
https://math.uchicago.edu/~may/REU2015/REUPapers/Ran.pdf
# Topological space
Let $X$ be a set. Let $τ$ be a collection of its subsets such that:
(1) the union of any collection of sets that are elements of $τ$ belongs to $τ$;
(2) the intersection of any finite collection of sets that are elements of $τ$ belongs to $τ$;
(3) the empty set $∅$ and the whole $X$ belong to $τ$.
Then
• $τ$ is a $topological$ $structure$ or just a $topology$ on $X$;
• the pair (X, Ω) is a $topological$ $space$;
• elements of $X$ are $points$ of this topological space;
• elements of $τ$ are $open$ $sets$ of the topological space $(X, τ)$.
The conditions in the definition above are the $axioms$ $of$ $topological$ $structure$.
# Algebraic Topology