Fully closed maps and non-metrizable higher-dimensional Anderson-Choquet continua

TL;DR

This paper uses fully closed maps to construct non-metrizable, higher-dimensional continua related to Anderson, Choquet, and Cook, and investigates their dimensional properties and dimension-lowering maps.

Contribution

It introduces new constructions of non-metrizable higher-dimensional continua using fully closed maps and proves theorems on dimension-lowering maps for broader classes of spaces.

Findings

Constructed non-metrizable higher-dimensional continua.

Proved theorems on dimension-lowering maps for non-hereditarily normal spaces.

Provided examples of continua with non-coinciding dimensions.

Abstract

Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for inductive dimensions and fully closed maps from spaces that need not be hereditarily normal, and some examples of continua have non-coinciding dimensions.