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...omplex number|complex]] numbers. Also note that any [[metric space]] is a uniform space. Finally, '''subheadings will always indicate special cases of thei ===...in a uniform space (''U'')=== ...

==Values in Banach spaces== ...he domain of ''f'', whereas the Bochner measurability of ''f'' is called ''uniform measurability'' (cf. "[[uniformly continuous]]" vs. "[[strongly continuous] ...

...alysis]] and related areas of [[mathematics]] a '''Brauner space''' is a [[Uniform space|complete]] [[compactly generated space|compactly generated]] [[locall ...an George Brauner], who began their study.{{sfn|Brauner|1973}} All Brauner spaces are [[stereotype space|stereotype]] and are in the stereotype duality relat ...

...], Delta-convergence and weak convergence coincide. For a general class of spaces, similarly to weak convergence, every bounded sequence has a Delta-converge == Characterization in Banach spaces == ...

...ok| last = Heinonen| first = Juha | title = Lectures on Analysis on Metric Spaces | series = Universitext | publisher = Springer-Verlag | location = New York ...nt/doi/10.1515/agms-2017-0004/html|journal=Analysis and Geometry in Metric Spaces|language=en|volume=5|issue=1|pages=69–77|doi=10.1515/agms-2017-0004|issn=22 ...

...d group''' is a [[topological group]] whose left and right [[uniform space|uniform structres]] coincide. ...e#Examples|right uniform structure]] and the [[Uniform space#Examples|left uniform structure]] of <math>G</math> are the same.<ref name="Arhangel’skii">{{cite ...

...nalysis]] and related areas of [[mathematics]], a '''Smith space''' is a [[Uniform space|complete]] [[compactly generated space|compactly generated]] [[locall Smith spaces are named after ...

...e non-continuous red function. This can happen only if convergence is not uniform.]] ...s]], the '''uniform limit theorem''' states that the [[uniform convergence|uniform limit]] of any sequence of [[continuous function]]s is continuous. ...

...in [[metric space]] that contains all [[separable space|separable]] metric spaces in a particularly nice manner. This [[mathematics]] concept is due to [[Pav ...''Urysohn universal''<ref>{{citation|title=Geometric embeddings of metric spaces|url=http://www.math.jyu.fi/research/reports/rep90.ps|author=Juha Heinonen|d ...

The product of any collection of quasi-complete spaces is again quasi-complete.{{sfn | Schaefer | Wolff | 1999 | p=27}} The projective limit of any collection of quasi-complete spaces is again quasi-complete.{{sfn | Schaefer | Wolff | 1999 | p=52}} ...

...athematics]], a '''quasi-ultrabarrelled space''' is a [[topological vector spaces]] (TVS) for which every [[Barrelled set|bornivorous ultrabarrel]] is a [[ne * [[Uniform boundedness principle#Generalisations]] ...

* {{annotated link|Topology of uniform convergence}} * {{Narici Beckenstein Topological Vector Spaces|edition=2}} <!-- {{sfn | Narici | 2011 | p=}} --> ...

...f [[mathematics]], an '''ultrabarrelled space''' is a [[topological vector spaces]] (TVS) for which every ultrabarrel is a [[Neighbourhood (topology)|neighbo * {{annotated link|Uniform boundedness principle#Generalisations}} ...

...ath> of [[real number]]s or [[complex number]]s. When equipped with the [[uniform norm]]: {{Banach spaces}} ...

In mathematics, a '''uniform matroid''' is a [[matroid]] in which the independent sets are exactly the s The uniform matroid <math>U{}^r_n</math> is defined over a set of <math>n</math> elemen ...

{{About|the vector spaces of sequences and functions|the finite-dimensional vector space distance|Che ...the latter. As a Banach space they are the continuous dual of the Banach spaces <math>\ell_1</math> of absolutely summable sequences, and <math>L^1 = L^1(X ...

...for any λ. Distortability first emerged as an important property of Banach spaces in the 1960s, where it was studied by {{harvtxt|James|1964}} and {{harvtxt| ...sup>''p''</sup>, all of which are [[separable metric space|separable]] and uniform convex, for {{nowrap|1 < ''p'' < &infin;}}. ...

...paces. He was one of the founders of modern descriptive theory of sets and spaces.<ref>Zdeněk Frolík 1933–1989, [[Mirek Husek]], [[Jan Pelant]], ''[[Topology ...ath>Y</math>.<ref>J.E. Vaughan, Countably compact and sequentially compact spaces. ''Handbook of Set-theoretic Topology'', [[Kenneth Kunen|K. Kunen]] and J. ...

...atural topology on <math>X^{\prime\prime}</math> (that is, the topology of uniform convergence on equicontinuous subset of <math>X^{\prime}</math>).{{sfn|Scha * {{Narici Beckenstein Topological Vector Spaces|edition=2}} <!-- {{sfn|Narici|Beckenstein|2011|p=}} --> ...

the [[uniform norm]]. The uniform norm defines the [[topology]] of [[uniform convergence]] of functions on <math>X.</math> The space <math>\mathcal{C}( ...X</math> and <math>Y</math> are [[homeomorphism|homeomorphic]] topological spaces. ...