# \v{C}ech border homology and cohomology groups and some applications

## TL;DR

This paper develops cech border homology and cohomology groups for closed pairs of normal spaces, providing intrinsic characterizations related to open coverings, cyclicity, and dimensions of Stone-cech remainders.

## Contribution

It introduces new cech border homology and cohomology groups and explores their applications in characterizing various topological properties.

## Key findings

- Characterization of cech homology and cohomology via border groups
- Connections between border groups and dimensions of Stone-cech remainders
- Applications to normal spaces and their compactifications

## Abstract

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.