Property C, Refinable Maps and Dimension Raising Maps

Abstract

Abstract. We show that refinable maps defined on compacta preserve Property C. H. Kato has proved the analogous result for weakly infinite dimensional spaces. We also show that if / is a map from a compact C space X onto a non C space Y, then the set of points in Y with an uncountable number of preimages is a space that does not have Property C.

Spaces whose 𝑛th power is weakly infinite-dimensional but whose (𝑛+1)th power is not

“…Garity, Hattori, Rohm, and Yamada (see [4,5,6,18,19]) have shown that in the presence of tr-compactness the products of spaces with property C behave in a regular way. Our examples, based on totally imperfect sets, lack compactness-like properties.…”