Find link

language: af: Afrikaans als: Alemannisch [Alemannic] am: አማርኛ [Amharic] an: aragonés [Aragonese] ar: العربية [Arabic] arz: مصرى [Egyptian Arabic] as: অসমীয়া [Assamese] ast: asturianu [Asturian] az: azərbaycanca [Azerbaijani] azb: تۆرکجه [Southern Azerbaijani] ba: башҡортса [Bashkir] bar: Boarisch [Bavarian] bat-smg: žemaitėška [Samogitian] be: беларуская [Belarusian] be-tarask: беларуская (тарашкевіца) [Belarusian (Taraškievica)] bg: български [Bulgarian] bn: বাংলা [Bengali] bpy: বিষ্ণুপ্রিয়া মণিপুরী [Bishnupriya Manipuri] br: brezhoneg [Breton] bs: bosanski [Bosnian] bug: ᨅᨔ ᨕᨘᨁᨗ [Buginese] ca: català [Catalan] ce: нохчийн [Chechen] ceb: Cebuano ckb: کوردیی ناوەندی [Kurdish (Sorani)] cs: čeština [Czech] cv: Чӑвашла [Chuvash] cy: Cymraeg [Welsh] da: dansk [Danish] de: Deutsch [German] el: Ελληνικά [Greek] en: English eo: Esperanto es: español [Spanish] et: eesti [Estonian] eu: euskara [Basque] fa: فارسی [Persian] fi: suomi [Finnish] fo: føroyskt [Faroese] fr: français [French] fy: Frysk [West Frisian] ga: Gaeilge [Irish] gd: Gàidhlig [Scottish Gaelic] gl: galego [Galician] gu: ગુજરાતી [Gujarati] he: עברית [Hebrew] hi: हिन्दी [Hindi] hr: hrvatski [Croatian] hsb: hornjoserbsce [Upper Sorbian] ht: Kreyòl ayisyen [Haitian] hu: magyar [Hungarian] hy: Հայերեն [Armenian] ia: interlingua [Interlingua] id: Bahasa Indonesia [Indonesian] io: Ido is: íslenska [Icelandic] it: italiano [Italian] ja: 日本語 [Japanese] jv: Basa Jawa [Javanese] ka: ქართული [Georgian] kk: қазақша [Kazakh] kn: ಕನ್ನಡ [Kannada] ko: 한국어 [Korean] ku: Kurdî [Kurdish (Kurmanji)] ky: Кыргызча [Kirghiz] la: Latina [Latin] lb: Lëtzebuergesch [Luxembourgish] li: Limburgs [Limburgish] lmo: lumbaart [Lombard] lt: lietuvių [Lithuanian] lv: latviešu [Latvian] map-bms: Basa Banyumasan [Banyumasan] mg: Malagasy min: Baso Minangkabau [Minangkabau] mk: македонски [Macedonian] ml: മലയാളം [Malayalam] mn: монгол [Mongolian] mr: मराठी [Marathi] mrj: кырык мары [Hill Mari] ms: Bahasa Melayu [Malay] my: မြန်မာဘာသာ [Burmese] mzn: مازِرونی [Mazandarani] nah: Nāhuatl [Nahuatl] nap: Napulitano [Neapolitan] nds: Plattdüütsch [Low Saxon] ne: नेपाली [Nepali] new: नेपाल भाषा [Newar] nl: Nederlands [Dutch] nn: norsk nynorsk [Norwegian (Nynorsk)] no: norsk bokmål [Norwegian (Bokmål)] oc: occitan [Occitan] or: ଓଡ଼ିଆ [Oriya] os: Ирон [Ossetian] pa: ਪੰਜਾਬੀ [Eastern Punjabi] pl: polski [Polish] pms: Piemontèis [Piedmontese] pnb: پنجابی [Western Punjabi] pt: português [Portuguese] qu: Runa Simi [Quechua] ro: română [Romanian] ru: русский [Russian] sa: संस्कृतम् [Sanskrit] sah: саха тыла [Sakha] scn: sicilianu [Sicilian] sco: Scots sh: srpskohrvatski / српскохрватски [Serbo-Croatian] si: සිංහල [Sinhalese] simple: Simple English sk: slovenčina [Slovak] sl: slovenščina [Slovenian] sq: shqip [Albanian] sr: српски / srpski [Serbian] su: Basa Sunda [Sundanese] sv: svenska [Swedish] sw: Kiswahili [Swahili] ta: தமிழ் [Tamil] te: తెలుగు [Telugu] tg: тоҷикӣ [Tajik] th: ไทย [Thai] tl: Tagalog tr: Türkçe [Turkish] tt: татарча/tatarça [Tatar] uk: українська [Ukrainian] ur: اردو [Urdu] uz: oʻzbekcha/ўзбекча [Uzbek] vec: vèneto [Venetian] vi: Tiếng Việt [Vietnamese] vo: Volapük wa: walon [Walloon] war: Winaray [Waray] yi: ייִדיש [Yiddish] yo: Yorùbá [Yoruba] zh: 中文 [Chinese] zh-min-nan: Bân-lâm-gú [Min Nan] zh-yue: 粵語 [Cantonese]

jump to random article

searching for Category of topological spaces 52 found (148 total)

alternate case: category of topological spaces

Classifying space (1,893 words) [view diff] exact match in snippet view article find links to article

homotopy category of topological spaces. The term classifying space can also be used for spaces that represent a set-valued functor on the category of topological

In the mathematical field of topology, a topological space is usually defined by declaring its open sets. However, this is not necessary, as there are

mathematics, a topological monoid is a monoid object in the category of topological spaces. In other words, it is a monoid with a topology with respect

algebra and geometry. The example that started the subject is the category of topological spaces with Serre fibrations as fibrations and weak homotopy equivalences

categories not necessarily of algebraic origin, for example the category of topological spaces. Let C be a category, co(C) and we(C) two classes of morphisms

theory, the fundamental groupoid is a certain functor from the category of topological spaces to the category of groupoids. [...] people still obstinately

theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor

corresponding homotopy category is equivalent to the familiar homotopy category of topological spaces. Formally, a simplicial set may be defined as a contravariant

locally compact, then X × − {\displaystyle X\times -} from the category of topological spaces always has a right adjoint H o m ( X , − ) {\displaystyle Hom(X

further, to very different kinds of categories, including the category of topological spaces. In algebra, the S-construction is a construction in algebraic

These singleton topological spaces are terminal objects in the category of topological spaces and continuous functions. No other spaces are terminal in that

pointed topological spaces to the category of groups. In the category of topological spaces (without distinguished point), one considers homotopy classes

well-established notions of subobject or quotient object. In the category of topological spaces, monomorphisms are precisely the injective continuous functions;

identity element. A topological group is a group object in the category of topological spaces with continuous functions. A Lie group is a group object in

pullback bundle can be carried out in subcategories of the category of topological spaces, such as the category of smooth manifolds. The latter construction

adjunction between the homotopy categories. For example, the category of topological spaces and the category of simplicial sets both admit Quillen model

earlier been studied for uniform spaces. Characterizations of the category of topological spaces Convergence space – Generalization of the notion of convergence

Tietze extension theorem can be used to show that an interval is an injective cogenerator in a category of topological spaces subject to separation axioms.

topological categories) are categories enriched over some convenient category of topological spaces, e.g. the category of compactly generated Hausdorff spaces.

Y.} As described in the article on characterizations of the category of topological spaces, if certain conditions are met then it is possible to define

{Top} } , where T o p {\displaystyle \mathbf {Top} } is the category of topological spaces. Moreover, there is a map γ : Δ → T o p {\displaystyle \gamma

and direct image functors itself defines a functor from the category of topological spaces to the category of categories: given continuous maps f: X →

{\displaystyle b_{G}} is a contravariant functor from Top (the category of topological spaces and continuous functions) to Set (the category of sets and functions)

{\displaystyle X} is free on the set X {\displaystyle X} in the category of topological spaces and continuous maps or in the category of uniform spaces and

forms a cofibrant replacement. In fact, if we work in just the category of topological spaces, the cofibrant replacement for any map from a point to a space

defines a covariant functor from the category of Δ-sets to the category of topological spaces. Geometric realization takes a Δ-set to a topological space

the category of rings if and only if X is cohopfian in the category of topological spaces, and R is cohopfian as a ring if and only if X is hopfian as

products. For example, a topological group is just a group in the category of topological spaces. Most of the usual algebraic systems of mathematics are examples

Another example of H-objects are H-spaces in the homotopy category of topological spaces Ho ( Top ) {\displaystyle {\text{Ho}}({\textbf {Top}})} . In

Another example of H-objects are H-spaces in the homotopy category of topological spaces Ho ( Top ) {\displaystyle {\text{Ho}}({\textbf {Top}})} . In

ISBN 978-0-387-90839-7 Mathematics portal Characterizations of the category of topological spaces Equivariant topology List of algebraic topology topics List

\\(X,x_{0})&\mapsto \pi _{1}(X,x_{0})\end{aligned}}} from the category of topological spaces together with a base point to the category of groups. It turns

only if they are homotopy-equivalent. Then a functor on the category of topological spaces is homotopy invariant if it can be expressed as a functor on

define a functor F from K {\displaystyle {\mathcal {K}}} to the category of topological spaces as follows. For any face X in K of dimension n, let F(X) = Δn

manifold, is up to diffeomorphism. Characterizations of the category of topological spaces Characterizations of the exponential function – Mathematical

\mathbb {R} ^{2}/\mathbb {Z} ^{2}.} Here the quotient is in the category of topological spaces, rather than groups or rings. On the other hand, the sphere

spaces and G : KHaus → Top be the inclusion functor to the category of topological spaces. Then G has a left adjoint F : Top → KHaus, the Stone–Čech compactification

example, an injective continuous map is a monomorphism in the category of topological spaces. For proving that, conversely, a left cancelable homomorphism

constructions are more precise than various completions of the category of topological spaces.) Grothendieck & Verdier 1972 Lawvere 1975 "Locales as geometric

make sense for metric spaces (e.g. completeness) to a broader category of topological spaces. In particular, to topological groups and topological vector

Similarly, replacing M f d {\displaystyle \mathrm {Mfd} } with the category of topological spaces, one obtains the definition of topological stack. Recall that

x\mapsto (x,0)} . Fibrations and cofibrations. Let Top be the category of topological spaces, and let C 0 {\displaystyle C_{0}} be the class of maps S n

bundles: the category of vector bundles V→S is a stack over the category of topological spaces S. A morphism from V→S to W→T consists of continuous maps from

category is equivalent to a full subcategory of the homotopy category of topological spaces, the subcategory of rational spaces. By definition, a rational

Convergence in Topological Spaces" Steenrod, N.E., A convenient category of topological spaces, Michigan Math. J., 14 (1967), 133-152. Trèves, François (2006)

See also ordinal-indexed sequence. Characterizations of the category of topological spaces Filter (set theory) – Family of sets representing "large" sets

topological spaces over X {\displaystyle X} , that is, the category of topological spaces together with fixed continuous maps to X {\displaystyle X}

elements are given by isomorphisms in C. A common example is the category of topological spaces and continuous maps, with the monoidal product given by the

the union of two separated subsets. Characterizations of the category of topological spaces Čech closure operator – Closure operatorPages displaying short

category of Euclidean spaces is a concrete category over the category of topological spaces; the forgetful (or "stripping") functor maps the former category

from the poset category of non-negative real numbers to the category of topological spaces and continuous maps. There are some advantages to the categorical

are not widely used or known about. Characterizations of the category of topological spaces Convergence space – Generalization of the notion of convergence