In this way we obtain an injective mapping
from [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let there be given an injective mapping
[??] [member of] [C.sup.3]([bar.[omega]]; [R.sup.3]), such that the two vectors
Every order embedding is necessarily an injective mapping
Suppose G is a [[LAMBDA].sup.[alpha]]-extension domain in [R.sup.n] and f is a K-quasiregular locally injective mapping
of G onto f(G) [subset] [R.sup.n].
An injective mapping (Equation) is called mean labeling of (Equation) if the induced edge function (Equation) defined as (Equation) is bijective.
An injective mapping is called mean labeling of (Equation) if the induced edge function (Equation) defined as
Since E([t.sup.+]) is a right zero band, s = [ss.sup.+] = [tft.sup.+] = [tt.sup.+] = t and hence [theta] is an injective mapping
If that is the case, then a subsequence of [f.sub.k] converges to some conformal injective mapping
[Mathematical Expression Omitted].
Lemma 7 There exists an injective mapping
f : [S.sub.1] [union] [S.sub.2] [right arrow] [B.sub.2] [union] [D.sub.2].
Recall that an embedding of a graph [GAMMA] in a graph [GAMMA]' is an injective mapping
of the vertex set of [GAMMA] to the vertex set of [GAMMA]' such that two vertices of [GAMMA] are adjacent if and only if their images are adjacent.