What question did this study set out to answer?

This research aims to investigate the partitioning of aposyndetic continua into subclasses and the existence of common models.

February 22, 2026Mathematica Slovaca0 citations

A study of aposyndetic continua: nonexistence of common models and mutual incomparability

EMEiichi MatsuhashiShimane University

Key Points

This research aims to investigate the partitioning of aposyndetic continua into subclasses and the existence of common models.
Partitioned aposyndetic continua using dimension as a criterion.
Identified countably many subclasses of aposyndetic continua.
Analyzed the existence of common models and mutual incomparability among continua.
Identified multiple subclasses with no common model, except for one possible exception.
Found a continuum-sized subfamily of mutually incomparable continua in these subclasses.
The status of the exceptional subclass regarding common models remains unresolved.

Abstract

Abstract In this paper, we show that the class of aposyndetic continua can be partitioned, using the notion of dimension, into countably many subclasses, each of which, except for one, has no common model and contains a continuum-sized subfamily of mutually incomparable continua. Whether a common model or a continuum-sized subfamily of mutually incomparable continua exists for this exceptional subclass remains open.

AI에게 질문

Bookmark

View Full Paper