Sentence examples for i a has from inspiring English sources

Then the following three conditions are equivalent: (i) A has the equicontinuity property for clc-spaces; (ii) A has the equicontinuity property for R; (iii) X is barrelled.

More generally (and more carefully) put: Necessarily, for any individual a, (i) a has a haecceity h and (ii) necessarily, h exists.

Suppose that (A:overline {U}rightarrow X) is a continuous, compact map, then either (i) A has a fixed point in U̅, or   (ii) there is a (uinpartial U) and (lambdain 0,1) ) with (u=lambda AU+ 1-lambda p).  .

Then either (i) A has a fixed point in U ¯, or   (ii) there is x ∈ ∂ U (the boundary of U in C) and λ ∈ ( 0, 1 ) with x = λ A ( x ).  .

Then either (i) A has a fixed point in U̅, or   (ii) there are (xinpartial U) (the boundary of U in C) and (muin ( 0,1 ) ) with (x=mu A x)).  .

Further, we assume that A is local, that is, (i) A has a unique maximal ideal (which we denote by ), and (ii) the natural injective homomorphism is in fact an isomorphism.

Connecticut (2-3) at Boston College (2-2) UConn's first season in Division I-A has been trying.

We show that the mapping PΘ γf + (I - A)) has a unique fixed point.

Step 4. We prove that the mapping PΘ γf + (I - A)) has a unique fixed point.

By using Theorem 2 in [18], we know that the operator (I + A) has a trivial null space in the weighted product space X.

Then, Banach's contraction mapping principle guarantees that P F (γ f +I - A) has a unique fixed point, say q ∈ H.