  In the paper the \v{C}ech border homology and cohomology groups of closed
pairs of normal spaces are constructed and investigated. These groups give
intrinsic characterizations of \v{C}ech homology and cohomology groups based on
finite open coverings, homological and cohomological coefficients of cyclicity,
small and large cohomological dimensions of remainders of Stone-\v{C}ech
compactifications of metrizable spaces.
