θ-continuous extensions of maps on τX
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CONTENTS1. Introduction...................................................52. ℬ-filters and ℬ-compactifications..................63. The weight of φX.........................................124. Other properties of φX................................155. Extensions of maps and subspaces............216. Subordinate subsets of C*(X)......................257. Quasi-component spaces...........................308. References.................................................33
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Let X be a space. A space Y is called an extension of X if Y contains X as a dense subspace. For an extension Y of X the subspace Y∖X of Y is called the remainder of Y. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X pointwise. For two (equivalence classes of) extensions Y and Y' of X let Y ≤ Y' if there is a continuous mapping of Y' into Y which fixes X pointwise. Let 𝓟 be a topological property. An extension Y of X is called a 𝓟-extension...