Reduction of Open Mappings

Reduction of Open Mappings

In 1936 G. T. Whyburn [8] defined an irreducible mapping to be a mapping/, of a compact metric continuum A onto B, such that no proper sub-continuum of A maps onto B under/. Similarly, assuming A to be only compact and metric, he defined / to be strongly irreducible provided that no closed proper subset of A maps onto B. J. Rozanska [7] independently defined this second type of mapping in 1937....

Open Mappings Increasing Order

It is shown that an analog of Whyburn’s theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is he...

Supervised dimension reduction mappings

Abstract. We propose a general principle to extend dimension reduction tools to explicit dimension reduction mappings and we show that this can serve as an interface to incorporate prior knowledge in the form of class labels. We explicitly demonstrate this technique by combining locally linear mappings which result from matrix learning vector quantization schemes with the t-distributed stochast...

Atomic Mappings Can Spoil Lightness of Open Mappings

We study continua on which each nonconstant open mapping is light. W. Makuchowski asked if this property is preserved under atomic mappings. It is known that this is true under an additional assumption of arcwise connectedness of the domain continuum. We show that in general this is not true.

A Characterization of Certain Quasi-open Mappings