1 Introduction ................................................. 5
2 Compactification-like  -extensions ........................... 7
3 Compactification-like -extensions with countable
remainder ................................................... 24
4 Compactification-like -extensions as partially ordered
sets ........................................................ 53
5 Applications ................................................ 82
5.1 Tight -extensions ..................................... 82
5.2 On a question of S. Mrówka and J.H. Tsai ............... 84
6 Question .................................................... 86
References ..................................................... 86
Index .......................................................... 88
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