If X is a topological space and Y is a ring of closed sets, then a necessary and sufficient condition for the Wallman space W(X,F) to be a compactification of X is that X be T1 andYF separating. A necessary and sufficient condition for a Wallman compactification to be Hausdoff is that F be a normal base. As a result, not all T, compactifications can be of Wallman type. One point and finite Hausdorff compactifications are of Wallman type.

The ideas that flourished among a small group of former Uppsala students that became the Göthiska förbundet on February 16, 1811, set in motion a process that changed views on why and how Sweden should manage its historic sites. This process of change achieved its goal with the passing of the new antiquities legislation in 1828. Their archeological research also left its mark. In this area, the brotherhood went much further than they themselves had actually imagined possible when they formulated their description of the ideal state consisting of free, independent farmers, which they believed was the case up until the introduction of Christianity into the Nordic countries. It was this period that they attributed the brotherhood’s virtues that they wished to instill in modern Swedes, and it was this image that would become part of the Swedish cultural heritage. Their archeological research, though, took them even further back in time. Geijer’s history books were admirable, but Magnus Bruzelius went the furthest. Starting with a study of historic sites, he extended the time period about which one could comment at great length, going as far back as to a period that did not even have a name, a period he called the Stone Age. As a result of this, their research demonstrated that the region’s oldest historic sites did not belong to sword-wielding free farmers, but rather to primitive Stone Age savages about whose living conditions Magnus Bruzelius could write because he was able to study their material remains and compare his findings with the commentaries by travelers to primitive peoples from other, more inaccessible parts of the globe. Accordingly, both time and research achieved new heights. / digitalisering@umu

Στα δύο πρώτα κεφάλαια γίνεται μια ιστορική αναδρομή και αναφέρονται όλες οι απαραίτητες εισαγωγικές έννοιες που χρειάζονται έτσι, ώστε να γίνει απρόσκοπτα και χωρίς ασάφειες το κυρίως μέρος της εργασίας. Στο κεφάλαιο τρία περιγράφονται και αναλύονται οι συμπαγείς τοπολογικοί χώροι. Κατά σειρά εξετάζονται οι συμπαγείς χώροι, οι συνεχείς απεικονίσεις πάνω σε συμπαγείς χώρους και τέλος οι τοπικά συμπαγείς χώροι. Επίσης περιγράφονται έννοιες συναφείς με τη συμπάγεια. Στο τέταρτο και τελευταίο κεφάλαιο ορίζεται η έννοια της συμπαγοποίησης ενός τοπολογικού χώρου και μελετώνται κατά σειρά η συμπαγοποίηση ενός σημείου, η συμπαγοποίηση Stone – Čech και η Wallman-type συμπαγοποίηση. / We study compact topological spaces. We also describe the compactification of a topological space. Especially we describe the Alexandroff, Stone-Cech and Wallman type compactifications.