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The presence of green spaces within city centres has been recognized as a valuable component of the city landscape. Vegetation provides a variety of benefits including energy saving, improved air q...

In this paper the notion of hyperconnectivity, which is an extension of connectivity is explored in the lattice theoretical framework. It is shown that a fourth axiom is needed when moving from connections to hyperconnections, in order to define hyperconnected components meaningfully, which is important for the definition of, e.g., viscous levellings. New hyperconnectivity openings, which are the hyperconnected equivalents of connectivity openings are then defined. It then shown that all algebraic openings which are translation and grey-scale invariant can be described as hyperconnected attribute filters. This means that hyperconnectivity lies at the heart of a vast range of morphological filters.