| 1. | Unlike the projective case, ideal points form a boundary, not a submanifold.
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| 2. | Increased product variety provides consumers with offerings nearer their ideal points.
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| 3. | Areas without ideal points are sometimes referred to as demand voids.
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| 4. | Some maps plot ideal vectors instead of ideal points.
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| 5. | Many perceptual maps also display consumers ideal points.
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| 6. | Human tears have a pH of 7.4, making this an ideal point to set a pool.
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| 7. | In the 19th century, the isolation made it an ideal point for the meetings of pugilists.
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| 8. | His book preaches the use of probabilities to determine ideal points to begin building a position.
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| 9. | In hyperbolic geometry an "'ideal triangle "'is a hyperbolic triangle whose three vertices all are ideal points.
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| 10. | The next diagram shows a study of consumers ideal points in the alcohol / spirits product space.
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