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Finite‐to‐One Mappings on Infinite‐dimensional Compacta
Author(s) -
POL ROMAN
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36810.x
Subject(s) - transfinite number , dimension (graph theory) , mathematics , pure mathematics , curse of dimensionality , statistics
Weakly infinite‐dimensional compacta can be classified by means of essential maps onto “transfinite cubes” (Smirnov's compacta). We investigate the behavior of this classification under finite‐to‐one mappings. In particular, we show that this topic is closely related to an open problem about the invariance of strong infinite‐dimensionality under light mappings on compacta. We provide also an analogue for the transfinite dimension ind of Hurewicz's the‐orem on dimension‐rising mappings.