Uniform property

In the mathematical field of topology a uniform property or uniform invariant is a property of a uniform space which is invariant under uniform isomorphisms.

Since uniform spaces come as topological spaces and uniform isomorphisms are homeomorphisms, every topological property of a uniform space is also a uniform property. This article is (mostly) concerned with uniform properties that are not topological properties.

Uniform properties

  • Separated. A uniform space X is separated if the intersection of all entourages is equal to the diagonal in X × X. This is actually just a topological property, and equivalent to the condition that the underlying topological space is Hausdorff (or simply T0 since every uniform space is completely regular).
  • Complete. A uniform space X is complete if every Cauchy net in X converges (i.e. has a limit point in X).
  • Totally bounded (or Precompact). A uniform space X is totally bounded if for each entourage E ⊂ X × X there is a finite cover {Ui} of X such that Ui× Ui is contained in E for all i. Equivalently, X is totally bounded if for each entourage E there exists a finite subset {xi} of X such that X is the union of all E[xi]. In terms of uniform covers, X is totally bounded if every uniform cover has a finite subcover.
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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Uniform_property

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    The Hindu 01 Apr 2025
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    The Times of India 31 Mar 2025
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    Deccan Herald 31 Mar 2025
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    The Times of India 30 Mar 2025
    ... Valuation Board was conducting a thorough assessment of the BMC property tax structure to prepare a new uniform property tax structure for all its 41 wards based on the Unit Area Assessment system.
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    The Gazette Cedar Rapids 30 Mar 2025
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    Do not rush to buy in the UK’s property market

    Taipei Times 29 Mar 2025
    Indices, such as those published by mortgage lenders Halifax and Nationwide, give a misleading picture of uniformity, distilling price movements across a wide variety of property types and tenures down to a single figure.
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    Interesting Engineering 28 Mar 2025
    This is essential to verify because impurities and structural defects in a material can affect its superconducting properties ... They also plan to study changes in superconducting properties upon application of uniform pressure to the material.
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    Craig City Councilor Randy Looper, representing Craig on the committee, pointed out that while Moffat County has a property tax, Craig does not, making it difficult to implement uniformly across all jurisdictions.
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    Hindustan Times 23 Mar 2025
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    Spring has sprung!

    Oelwein Daily Register 23 Mar 2025
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    The fight against blight

    Greenville Daily News 20 Mar 2025
    Montcalm County Sheriff Mike Williams, right, shares his thoughts about creating a uniform ordinance for townships to adopt regarding blighted properties, which the Sheriff’s Office would then enforce.
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    ‘An absolute mess’: Residents of Morton County reflect on pipeline protests years later

    Knoxville Daily Sun 20 Mar 2025
    Camisa told The Center Square her husband served as civilian staff for the Mandan Police Department at the time, enforcing municipal codes for things like property maintenance. But he still wore a kind of officer uniform, which made Camisa nervous ... +7.
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    The Stranger 19 Mar 2025
    by Vivian McCall ... Tiny homes can be manufactured in weeks and existing property can be leased and converted ... (Though a vacancy tax may fly afoul of the state constitution’s uniformity clause. In Washington, all properties must be taxed equally).

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