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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14404 |
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Table of Contents:
- We introduce the set-self-Tietze property, an analogue of the self-Tietze property for upper semi-continuous set-valued functions. A topological space $X$ is self-Tietze, if for every closed $A \subseteq X$ and continuous function $f \colon A \to X$, there is a continuous extension $F \colon X \to X$ of $f$. A topological space $X$ is set-self-Tietze, if for every closed $A \subseteq X$ and upper semi-continuous set-valued function $f \colon A \to 2^X$, there exists an upper semi-continuous set-valued function $F \colon X \to 2^X$ such that $\left. F \right|_A = f$. We show every compact metric space is set-self-Tietze, and that the torus is not self-Tietze.