Isotoping Mappings to 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...

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.

Mappings to Realcompactifications

In this paper, we introduce and study  a mapping from the collection of all  intermediate rings of $C(X)$ to the collection of all  realcompactifications of $X$ contained in $beta X$. By establishing the relations between this mapping and its converse,  we give a different approach to the main statements of De et. al. Using these, we provide different answers to the   four basic questions...

A Characterization of Certain Quasi-open Mappings