the edge or margin of a steep place or of land bordering water.

any extreme edge; verge.

a crucial or critical point, esp. of a situation or state beyond which success or catastrophe occurs

We were on the brink of war.

noun

center , interior , middle

noun

border , boundary , brim , fringe , frontier , limit , lip , margin , perimeter , periphery , point , rim , skirt , threshold , verge , borderline , edge , edging , bank , bluff , circumference , crest , end , eve , extremity , line , precipice , ridge , sea , shore , tip , top