Gespeichert in:
| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.03380 |
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Inhaltsangabe:
- The purpose of this paper is to find conditions for a continuous onto map $ϕ\colon X\rightarrow Y$ and its induced map $ϕ_*\colon\mathcal{M}^1(X)\rightarrow\mathcal{M}^1(Y)$ to be semi-open, where $X$, $Y$ are compact Hausdorff spaces and $\mathcal{M}^1(X)$, $\mathcal{M}^1(Y)$ are their Borel probability spaces. For that, we mainly prove the following results by using the structure theory of extensions of semiflows and inverse limit techniques: (1) If $ϕ$ is an extension of minimal flows, then $ϕ_*$ is semi-open. (2) If $ϕ$ is a quasi-separable fiber-onto extension of minimal semiflows, then $ϕ$ and $ϕ_*$ are semi-open. (3) If $Y$ is metrizable, then $ϕ$ is semi-open if and only if $ϕ_*$ is semi-open. In addition, if $X,Y$ are left-topological groups, $X$ is Lindelöf quasi-regular, $Y$ is Baire and if $ϕ$ is a locally closed continuous onto equivariant mapping, then $ϕ$ is semi-open (This is a generalization of Pontryagin's open-mapping theorem).