This text bridges the gap existing in the field of set theoretical
topology between the introductory texts and the more specialised
monographs. The authors review fit developments in general topology
and discuss important new areas of research and the importance of
defining a methodology applicable to this active field of
mathematics. The concept of normal cover and related ideas is
considered in detail, as are the characterisations of normal
spaces, collectionwise normal spaces and their interrelationships
with paracompact spaces (and other weaker forms of compactness).
Various methods of embedding subspaces are studied, before
considering newer concepts such as M-spaces and their relationships
with established ideas. These ideas are applied to give new results
pertaining to the extension of continuous vector-valued functions.
Wallman Frink compactifications and realcompactifications are also
studied to assist in unifying the ideas through the use of the more
general L-filter.
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