Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
The collection \(\{a\} \times (b, c) \subseteq \mathbb{R}^2 \mid a, b, c \in \mathbb{R}\) of vertical intervals in the plane is a basis for a topology on \(\mathbb{R}^2\). We call this topology the **vertical interval topology**.
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Transcribed Image Text:The collection \(\{a\} \times (b, c) \subseteq \mathbb{R}^2 \mid a, b, c \in \mathbb{R}\) of vertical intervals in the plane is a basis for a topology on \(\mathbb{R}^2\). We call this topology the **vertical interval topology**.
Compare the vertical interval topology with the standard topology on \( \mathbb{R}^2 \). Which one is finer, the vertical interval topology on \( \mathbb{R}^2 \) or the standard topology on \( \mathbb{R}^2 \)?
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Transcribed Image Text:Compare the vertical interval topology with the standard topology on \( \mathbb{R}^2 \). Which one is finer, the vertical interval topology on \( \mathbb{R}^2 \) or the standard topology on \( \mathbb{R}^2 \)?
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