Search arXivSearch

arXiv · math/0312456

Problems from Topology Proceedings

Abstract

This book consists of material originally appearing in the Problem Section of the journal Topology Proceedings since 1976 as well as some other well-known problem lists in general topology from the 1970's that have some connection to the journal. The problems have been updated with current information on solutions with bibliographic references. In particular, the book features these collections: All contributed problems to the Problem Section, classified by subject; Eight Classic Problems by Peter J. Nyikos, including information from the two recent articles Twenty-five years later; New Classic Problems from 1990; Problems from Mary Ellen Rudin's Lecture notes in set-theoretic topology (1975/7); Problems from A.V. Arhangelskii's Structure and classification of topological spaces and cardinal invariants (1978); Continuum theory problems by Wayne Lewis (1983); Problems in continuum theory by Janusz R. Prajs, including essays by Charles L. Hagopian and Janusz J. Charatonik; Classification of homogeneous continua by James T. Rogers, Jr., including material from survey articles of 1983 and 1989.

Explore related subjects

Keep this discovery

BibTeXRIS

Elliott Pearl. 2003-12-25. Problems from Topology Proceedings. https://arxiv.org/abs/math/0312456

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Maximal Center of Distances of Finite Ultrametric Spaces and Perfect Binary Trees

We investigate the finite ultrametric spaces $(X,d)$ that have a given cardinality of the center of distances and a minimal cardinality of the set $X$. It is shown that such spaces are isometric if and only if their centers of distances are the same. The representing trees of these spaces are characterized up to isomorphism.

math.GN

A continuous $3$-distributive frame that is not $\omega$-distributive

We give a negative answer to the question, posed by Ern\'e, whether every $3$-distributive lattice is $\omega$-distributive. More precisely, we exhibit a continuous frame that is $\kappa$-distributive for every integer $\kappa\geq 2$, but is not a wide coframe. The frame is the open-set lattice of a compact, locally compact, countably based $T_0$ topological meet-semilattice, obtained from Lawson's construction in the logarithmic form described by Goubault-Larrecq. The failure of $\omega$-distributivity is witnessed by an explicit matrix with countably many nonempty finite rows: all row joins are the same nonzero element, whereas every choice of one entry from each row has meet zero. The same space answers negatively Ern\'e's accompanying question whether every $4$-web space is a wide web space. All properties of the construction needed for these conclusions are proved directly.

math.GN

An overlooked weakening of perfect normality: Perfect regularity in spaces and locales

We introduce the notion of perfect regularity as an appropriate weakening of perfect normality, both for spaces and locales. Various characterizations are given, using Dedekind-MacNeille completions, injective hulls, and sublocales. We place the new class of perfectly regular frames among various well-studied classes of frames. We also introduce the construction of perfect regularization of a completely regular frame, compare it to Isbell's well-known booleanization construction, and argue that it is at least as important as the latter.

math.GN