Abstract
It is well known that ifX andY are completely regularT 2 spaces, then any continuous function,f, fromX toY, has a unique continuous extension,β(f), fromβX toβY, whereβX andβY are the Stone—Čech compactifications ofX andY, respectively. This function plays an important role in Stone—Čech Theory, especially in questions pertaining to embeddability.
In this paper, we first extend this construction to general Wallman spaces, and then apply the results to extend well-known embeddability theorems.
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Bachman, G., Stratigos, P.D. On an extension of a lattice-continuous mapping with embeddability applications. Period Math Hung 16, 237–244 (1985). https://doi.org/10.1007/BF01848073
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DOI: https://doi.org/10.1007/BF01848073