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

4 votes
1 answer
489 views

A question on PL-topology and polytopal complex

Question : $C$ is a pure, full-dimensional polytopal complex(a special case of a regular cell complex) in $\mathbb{R}^d$. I know that the boundary of the underlying set is a PL-sphere. Is it true that …
2 votes
0 answers
185 views

Simple topological question on taking complements inside a simplex

We would like to know if the following claim is true: (If you don't know the definition of a tropical hyperplane, then please consider the case when d=3) Let $P_1,\cdots,P_d$ be full dimensional (pos …