A connector, comprising: at least one terminal fitting; and a housing including at least one cavity into which the terminal fitting fixed to a wire is to be at least partly inserted; wherein: the terminal fitting includes a wire connection portion to be fixed to a core of the wire and a contact part between the wire connection portion and the core of the wire is covered by a fluidproof member; and a recess for widening the width of the cavity is formed in a part of a side wall of the cavity substantially corresponding to the wire connection portion of the terminal fitting, wherein the terminal fitting includes a connecting portion to be connected to a mating terminal fitting and a linking portion linking the wire connection portion and the connecting portion, characterized in that the recess includes a pair of recesses formed on substantially opposite side surfaces of the side wall partitioning between adjacent cavities; the fluidproof member comprises a heat shrinking tube and at least partly covers an outer side of the linking portion; and the linking portion includes a fluidproof portion for at least partly filling up a clearance between the linking portion and the fluidproof member. at least one terminal fitting; and a housing including at least one cavity into which the terminal fitting fixed to a wire is to be at least partly inserted; wherein: the terminal fitting includes a wire connection portion to be fixed to a core of the wire and a contact part between the wire connection portion and the core of the wire is covered by a fluidproof member; and a recess for widening the width of the cavity is formed in a part of a side wall of the cavity substantially corresponding to the wire connection portion of the terminal fitting, wherein the terminal fitting includes a connecting portion to be connected to a mating terminal fitting and a linking portion linking the wire connection portion and the connecting portion, characterized in that the recess includes a pair of recesses formed on substantially opposite side surfaces of the side wall partitioning between adjacent cavities; the fluidproof member comprises a heat shrinking tube and at least partly covers an outer side of the linking portion; and the linking portion includes a fluidproof portion for at least partly filling up a clearance between the linking portion and the fluidproof member. the terminal fitting includes a wire connection portion to be fixed to a core of the wire and a contact part between the wire connection portion and the core of the wire is covered by a fluidproof member; and a recess for widening the width of the cavity is formed in a part of a side wall of the cavity substantially corresponding to the wire connection portion of the terminal fitting, wherein the terminal fitting includes a connecting portion to be connected to a mating terminal fitting and a linking portion linking the wire connection portion and the connecting portion, characterized in that the recess includes a pair of recesses formed on substantially opposite side surfaces of the side wall partitioning between adjacent cavities; the fluidproof member comprises a heat shrinking tube and at least partly covers an outer side of the linking portion; and the linking portion includes a fluidproof portion for at least partly filling up a clearance between the linking portion and the fluidproof member.