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This analysis explores how retraction maps affect numerical invariants in topological spaces, indicating potential stability in their inequalities.
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category, the topological complexity, and the sequential topological complexity. We prove that, under the retraction map, the corresponding inequalities between invariants hold. Our results also apply to recent invariants are defined by Dranishnikov, Jauhari {DJ} and Knudsen, Weinberger {KW}.
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Nursultan Kuanyshov (2025) studied this question.
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