Date of Graduation

Spring 2026

Document Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Committee Chairperson

Jeremy Brazas, PhD

Committee Member

Michael Fisher, PhD

Committee Member

Scott Parsell, PhD

Abstract

Gluing constructions such as pushouts and other colimits are often used to attach spaces to- gether in algebraic topology. The weak topology is a natural choice of topology for attachment spaces in the context of CW-complexes and simplicial complexes because of its universal property but is insufficient for gluing together infinitely many spaces and preserving topological properties like compactness or metrizability. In this thesis, we introduce a modification of the weak topology called the shrinking attachment topology, which is defined on a space Y constructed by attaching an infinite sequence of spaces B1, B1, B3, . . . to a given core space X using a sequence of attachment maps. We show that shrinking attachment spaces have their own universal property and can be used to construct familiar locally complicated spaces. Moreover, we show that many topological properties such as compactness and metrizability are inherited by Y from the core and attachment spaces.

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