Sentence examples for maps f in from inspiring English sources

The class W of maps f in ({mathcal {D}}) whose cone ({text {Cone}}(f)) lies in ({mathcal {D}}_0) is saturated in the sense of Definition 2.2.

In this paper, we extend and prove Ky Fan's Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions.

(i) The class W of maps f in ({mathcal {D}}) whose cone ({text {Cone}}(f)) lies in ({mathcal {D}}_0) is saturated in the sense of Definition 2.2.   (ii) Assume that the relative category (langle {mathcal {D}},W rangle ) is localizable in the sense of Definition 2.4.

For any good model prefibration (mathcal {C}) over a Reedy category I with the matching expansion (rho :M(I) rightarrow I), a derived section (sigma ) of (mathcal {C}) over I is a section (sigma in {text {Sec}}(M(I),rho ^*mathcal {C})) that is homotopy cartesian along all maps f in M(I) vertical with respect to (rho ).

Denote by (lambda :I_L rightarrow I), (mu :I_M rightarrow I) the embedding functors, let (widetilde{C}) be class of maps f in (mathcal {C}^I) such that (lambda ^* f)) is a cofibration with respect to the projective model structure of Definition 2.7, and let (widetilde{F}) be the class of maps f such that (mu ^* f)) is a fibration with respect to the injective model structure of Definition 2.7.

A map f in ((Delta X)^o) is special resp.

Let the map F in the case γ = 0 be denoted by F | γ = 0.

In this part we study some particular forms of the mapping f in (1).

Say that a map f in (mathsf{G}(L,M,q)) is in C resp.

Furthermore, for any map f in (Delta _flat X) that is vertical resp.

Remark 3.3 We obtain that the mapping F in Example 3.1 has a coupled fixed point.