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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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Filtered colimit of a topological space

Suppose that $X$ is a space filtered by closed subspaces $X_{1}\subset X_{2}\subset \dots$. As topological space $X=\operatorname{colim}_{n}X_{n}$. We define $Y_{n}=X_{n+1}/X_{n}$, and consider the …