End-fray resistant heat-shrinkable woven sleeve, assembly therewith and methods of construction thereof

1. A method of constructing a flexible textile sleeve assembly, comprising:

providing an elongate member;

weaving an elongate wall having a circumferentially closed wall extending lengthwise along a central axis between opposite ends by weaving warp yarn extending generally parallel to the central axis with weft yarn including at least one heat-shrinkable weft yarn extending generally transversely to the warp yarn with at least one of the warp or weft yarns having a diameter between about 0.20-0.40 mm including at least one melt, heat-fusible yarn having a diameter between about 0.05-0.10 mm served thereabout;

at least partially melting the at least one low melt, heat-fusible yarn at a first temperature without substantially shrinking the at least one heat-shrinkable weft yarn;

cutting the wall to length;

disposing the elongate member in a cavity of the wall; and

heating the at least one heat-shrinkable weft yarn in the wall to a second temperature greater than said first temperature and shrinking the wall about the elongate member.