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...K-space''' is an [[F-space]] <math>V</math> such that every extension of F-spaces (or twisted sum) of the form ...ial one<ref name="kalton">Kalton, N. J.; Peck, N. T.; Roberts, James W. An F-space sampler. London Mathematical Society Lecture Note Series, 89. Cambrid ...

==Values in Banach spaces== For a function ''f'' with values in a [[Banach space]] (or [[Fréchet space]]), ''strong measur ...

...from <math>(X,A)</math> to <math>(X',A')</math> is given by two maps <math>f\colon X\rightarrow X'</math> and <math>g\colon A \rightarrow A'</math> such that <math> i' \circ g =f \circ i </math>. ...

...cepts are different. The relationship between the sub-Stonean spaces and F-spaces is studied in Henriksen and Woods, 1989. ...orona set]]s of locally compact σ-compact Hausdorff spaces are sub-Stonean spaces. ...

...vector <math>x \in X</math> satisfies <math>f(x) = 0</math> for all <math>f \in T,</math> then <math>x = 0</math> is the zero vector.<ref name=Klauder2 * {{annotated link|Topologies on spaces of linear maps}} ...

...hbb{F}</math>, then the bilinear map <math>X \times X^{\prime} \to \mathbb{F}</math> defined by <math>\left( x, x^{\prime} \right) \mapsto \left\langle ...first1=Nicolas | author1-link=Nicolas Bourbaki | title=Topological vector spaces | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Elemen ...

{{Short description|Generalization of Sobolev spaces}} ...ace which is a [[Banach space]] when {{math|1 ≤ ''p'', ''q'' ≤ ∞}}. These spaces, as well as the similarly defined [[Triebel–Lizorkin space]]s, serve to gen ...

...results about isomorphic measurable spaces, see [[Borel set#Standard Borel spaces and Kuratowski theorems|Kuratowski's theorem]]. However, (a) the latter the ...h> be measurable spaces. If there exist injective, bimeasurable maps <math>f : X \to Y, </math> <math>g : Y \to X, </math> then <math>X</math> and <math ...

In mathematics, '''amalgam spaces''' categorize functions with regard to their local and global behavior. Wh ...\|\cdot \|_X </math>. Then the ''Wiener amalgam space''<ref>Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis by Hans Georg Feichtinger an ...

...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 ...

...[Polish space]]. Except in the case of [[discrete space|discrete]] Polish spaces, the standard Borel space is unique, up to [[isomorphism]] of [[measurable ...ces have several useful properties that do not hold for general measurable spaces. ...

...sts some <math>b_0 \in B</math> such that <math>|f(b_0)| = \sup_{b \in B} |f(b)|</math>) <math display=block>\left\{f \in X^* : f \text{ attains its supremum on } B\right\}</math> ...

...86(2):307–340, 1989.</ref><ref>H. G. Feichtinger and K. Gröchenig. "Banach spaces related to integrable group representations and their atomic decompositions ...ly. Representation theory yields the reproducing formula <math>V_g f = V_g f * V_g g</math>. By [[discretization]] of this continuous [[convolution]] in ...

...f><ref>{{cite web|last=Strickland|first=Neil P.|title=The category of CGWH spaces|year=2009|url=http://neil-strickland.staff.shef.ac.uk/courses/homotopy/cgwh ...logy]]. For that, see the [[category of compactly generated weak Hausdorff spaces]]. ...

...basis. By [[Hahn–Banach theorem]] each ''e''^''i'' extends to ''f'' ^''i'' ∈ ''X''* such that : ||''f'' ^''i''|| = 1. ...

...Numbers in Weighted Function Space of Type <math>B^s_{pq}</math> and <math>F^s_{pq}</math>, Eigenvalue Distributions of Some Degenerate Pseudodifferenti In 2018, she was given a chair for function spaces at the [[University of Rostock]] before returning to her present position i ...

Similarly, '''quasibarrelled spaces''' are [[topological vector spaces]] (TVS) for which every [[bornivorous]] barrelled set in the space is a [[N Quasibarrelled spaces are studied because they are a weakening of the defining condition of [[bar ...

...morphism]] ''&fnof;'' is an [[identity (mathematics)|identity]] whenever ''F&fnof;'' is an identity. ...th [[continuous function]]s for morphisms to the [[category of topological spaces]]. If <math>d_1</math> and <math>d_2</math> are [[equivalent metrics]] on a ...

...ort description|Endofunctor on the category V of finite-dimensional vector spaces}} ...of finite-dimensional vector spaces]] that depends polynomially on vector spaces. For example, the [[symmetric power]]s <math>V \mapsto \operatorname{Sym}^n ...

In [[mathematics]], '''perfectoid spaces''' are [[adic space]]s of special kind, which occur in the study of problem ...olze]].<ref>{{cite journal | last=Scholze | first=Peter | title=Perfectoid spaces | journal=Publ. Math. Inst. Hautes Études Sci. | volume=116| pages=245–313 ...