Sentence examples for compact if it from inspiring English sources

Recall that the operator is called image compact if it is continuous and its image is a relatively compact set.

Recall that L X X → Y is metrically compact if it maps bounded sets into relatively compact sets.

The operator (L Xrightarrow Y) is said to be compact if it maps bounded sets into relatively compact sets.

Moreover, T : X → Y is said to be compact if it takes bounded sets in X to sets in Y which have compact closure.

Recall that a mapping between Banach spaces is compact if it is continuous and carries bounded sets into relatively compact sets.

A family of processes { U σ ( t, τ ) } σ ∈ Σ is called ( X, Y ) -uniformly asymptotically compact if it possesses a compact ( X, Y ) -uniformly (w.r.t.

ws-compact if it is continuous and maps relatively weakly compact sets of (mathcal{D}) into relatively strongly compact ones of Y; ww-compact if it is continuous and maps relatively weakly compact sets of (mathcal{D}) into relatively weakly compact ones of Y. Next, we collect a few auxiliary facts concerning the superposition operator required in the sequel.

A mapping (T:mathcal {D}subseteq Xrightarrow Y) is said to be: (i) ws-compact if it is continuous and maps relatively weakly compact sets of (mathcal{D}) into relatively strongly compact ones of Y;   (ii) ww-compact if it is continuous and maps relatively weakly compact sets of (mathcal{D}) into relatively weakly compact ones of Y.  .

A multivalued mapping F : X ⊸ Y is called compact if the set F ( X ) = ⋃ x ∈ X F ( x ) is contained in a compact subset of Y; it is called quasi-compact if it maps compact sets onto relatively compact sets; and completely continuous if it maps bounded sets onto relatively compact sets.

A multivalued mapping F : X ⊸ Y is called compact if the set F ( X ) = ⋃ x ∈ X F ( x ) is contained in a compact subset of Y and it is called quasi-compact if it maps compact sets onto relatively compact sets.

But some companies are happy to put you in a bigger, or less popular, vehicle for the cost of a compact -- if it's in their interest.