Property C and closed maps
A standard theorem from dimension theory states that a closed \((m+1)\) to 1 map defined on a finite dimensional space can raise dimension by at most m. Dimension raising maps on countable dimensional spaces and on weakly infinite dimensional spaces have been investigated by A. V. Arkhangelskij, A. I. Vajnshtejn and E. G. Sklyarenko. A typical theorem is that a closed map on such spaces raises dimension only if some point has an uncountable number of preimages. A class of infinite dimensional spaces closely related to the two types mentioned above is the class of C spaces. R. Pol's example in 1980 and recent work of F. D. Ancel have generated renewed interest in C spaces. The author proves results about dimension raising maps on C spaces analogous to the results mentioned above.
scientific article; zbMATH DE number 3984091