Matches in SemOpenAlex for { <https://semopenalex.org/work/W1994581034> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W1994581034 endingPage "100" @default.
- W1994581034 startingPage "87" @default.
- W1994581034 abstract "Introduction. This paper contains a detailed discussion with proofs of results announced in [4]. Let Mn and Nn be n-manifolds without boundary, and let f: Mn -+ N n be continuous. The map f is open if, whenever U is open in Mn, f(U) is open in Nn; it is light if, for every y e Nn ,dim (f'(y)) < 0. For n ? 2 there is a canonical light open map Fn,d: E giveni by Fn,d(Xl, x2, ..., Xn) = (u1, u2, x3 *, xv) where Ul + iU2 =(Xl t+ iX2 )d (i =Vi-1; d= 1,2, ... ). For n = 2 it is well known that a nonconstant complex analytic function is open and light. Conversely, Stoilow [12] proved that every light open map is locally topologically equivalent to an analytic map, and thus to some F2,d (d = 1,2, ... ). In fact (1.10), if M2 is compact and f is C2 and open, then f has this canonical structure. The main object of this paper is to prove (2.1) that the corresponding conclusion holds for arbitrary n (n _ 2), if we first remove an exceptional set of dimension at most n 3. Examples are given, especially in ?3, showing that the exceptional set and some of the hypotheses used are necessary. DEFINITION. As in [5] the branch set Bf is the set of points in Mn at which f fails to be a local homeomorphism. NOTATION. Iff : E nEP is C', then fi will be the ith component real-valued function, and Djfi will be the first partial derivative offi with respect to its jth coordinate. If y is a point in En, then yi will be its ith coordinate. The symbols Mn and NP will refer to manifolds of dimensions n and p, respectively. The statement that f: Mn -+ Np is Cm will imply that the manifolds are also Cm. The set of points in Mn at which the Jacobian matrix of f has rank at most q will be denoted by Rq. The closure of a set X is denoted by Cl[X] or X, its interior by int X, and the" @default.
- W1994581034 created "2016-06-24" @default.
- W1994581034 creator A5027523745 @default.
- W1994581034 date "1963-01-01" @default.
- W1994581034 modified "2023-10-16" @default.
- W1994581034 title "Differentiable open maps on manifolds" @default.
- W1994581034 cites W1974672421 @default.
- W1994581034 cites W1976723766 @default.
- W1994581034 cites W1995860445 @default.
- W1994581034 cites W2005898260 @default.
- W1994581034 cites W2007228790 @default.
- W1994581034 cites W2009013459 @default.
- W1994581034 cites W2043013923 @default.
- W1994581034 cites W2044034372 @default.
- W1994581034 cites W2063678770 @default.
- W1994581034 cites W2316420424 @default.
- W1994581034 cites W2600749203 @default.
- W1994581034 cites W4229922284 @default.
- W1994581034 cites W4245157187 @default.
- W1994581034 cites W4249242747 @default.
- W1994581034 cites W4255077432 @default.
- W1994581034 cites W2032770100 @default.
- W1994581034 doi "https://doi.org/10.1090/s0002-9947-1963-0154296-6" @default.
- W1994581034 hasPublicationYear "1963" @default.
- W1994581034 type Work @default.
- W1994581034 sameAs 1994581034 @default.
- W1994581034 citedByCount "32" @default.
- W1994581034 countsByYear W19945810342012 @default.
- W1994581034 countsByYear W19945810342016 @default.
- W1994581034 countsByYear W19945810342017 @default.
- W1994581034 countsByYear W19945810342019 @default.
- W1994581034 countsByYear W19945810342020 @default.
- W1994581034 countsByYear W19945810342021 @default.
- W1994581034 countsByYear W19945810342022 @default.
- W1994581034 crossrefType "journal-article" @default.
- W1994581034 hasAuthorship W1994581034A5027523745 @default.
- W1994581034 hasBestOaLocation W19945810341 @default.
- W1994581034 hasConcept C12520029 @default.
- W1994581034 hasConcept C195065555 @default.
- W1994581034 hasConcept C202444582 @default.
- W1994581034 hasConcept C202615002 @default.
- W1994581034 hasConcept C203934109 @default.
- W1994581034 hasConcept C2524010 @default.
- W1994581034 hasConcept C33923547 @default.
- W1994581034 hasConcept C516171914 @default.
- W1994581034 hasConceptScore W1994581034C12520029 @default.
- W1994581034 hasConceptScore W1994581034C195065555 @default.
- W1994581034 hasConceptScore W1994581034C202444582 @default.
- W1994581034 hasConceptScore W1994581034C202615002 @default.
- W1994581034 hasConceptScore W1994581034C203934109 @default.
- W1994581034 hasConceptScore W1994581034C2524010 @default.
- W1994581034 hasConceptScore W1994581034C33923547 @default.
- W1994581034 hasConceptScore W1994581034C516171914 @default.
- W1994581034 hasIssue "1" @default.
- W1994581034 hasLocation W19945810341 @default.
- W1994581034 hasOpenAccess W1994581034 @default.
- W1994581034 hasPrimaryLocation W19945810341 @default.
- W1994581034 hasRelatedWork W1540184672 @default.
- W1994581034 hasRelatedWork W1589781864 @default.
- W1994581034 hasRelatedWork W1972082663 @default.
- W1994581034 hasRelatedWork W2019580764 @default.
- W1994581034 hasRelatedWork W2084345112 @default.
- W1994581034 hasRelatedWork W2320181800 @default.
- W1994581034 hasRelatedWork W2332201812 @default.
- W1994581034 hasRelatedWork W2962966565 @default.
- W1994581034 hasRelatedWork W4240651083 @default.
- W1994581034 hasRelatedWork W972173259 @default.
- W1994581034 hasVolume "109" @default.
- W1994581034 isParatext "false" @default.
- W1994581034 isRetracted "false" @default.
- W1994581034 magId "1994581034" @default.
- W1994581034 workType "article" @default.