Title
The Scale of a Quasiuniform Space,Used
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We continue our investigations of the scale of a quasiuniform space, which we had started in an earlier article. We distinguish between the leftsided scale and the twosided scale of a quasiuniform space. While the behavior of the twosided scale of a quasiuniform space X shows similarities with the usual hyperspace of X equipped with its Hausdorff quasiuniformity, the lefthanded scale generalizes the quasiuniform multifunction space of X into itself.For instance the twosided scale of any totally bounded quasiuniform space X is totally bounded, while total boundedness of the leftsided scale of a quasiuniform space X implies that X is finite or indiscrete. Either construction of the scale is based on the idea of the prefilter space of a quasiuniform space. Prefilter spaces of quasiuniform spaces are shown to be bicomplete. It follows that both the leftsided and the twosided scale of a quasiuniform space are bicomplete. Indeed these scales can be used to construct the bicompletion of the T0reflection of the Hausdorff quasiuniformity of a quasiuniform space.
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Shipping & Returns
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We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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