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Lecture

Attachment of a 1-cell

In course

MATH-225: Topology II - fundamental groups

On étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre le Théorème de Seifert-van Kampen. Des exemples de surf ...

Description

This lecture discusses the attachment of a 1-cell to a space, focusing on the conditions for two points to belong to the same connected component. The lecture provides evidence and proofs for the attachment process, demonstrating how homotopy plays a crucial role in determining the relationship between points. Through detailed explanations and examples, the instructor illustrates the significance of well-pointedness and the implications for the attachment of cells in a space.

Instructors (2)

Jérôme Scherer

Dimitri Stelio Wyss

Official source

Related concepts (25)

Attachment theory

Attachment theory is a psychological, evolutionary and ethological theory concerning relationships between humans. The most important tenet is that young children need to develop a relationship with at least one primary caregiver for normal social and emotional development. The theory was formulated by psychiatrist and psychoanalyst John Bowlby. Within attachment theory, infant behaviour associated with attachment is primarily the seeking of proximity to an attachment figure in stressful situations.

Homotopy group

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space. To define the n-th homotopy group, the base-point-preserving maps from an n-dimensional sphere (with base point) into a given space (with base point) are collected into equivalence classes, called homotopy classes.

Homotopy theory

In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topology, the theory has also been used in other areas of mathematics such as algebraic geometry (e.g., A1 homotopy theory) and (specifically the study of ). In homotopy theory and algebraic topology, the word "space" denotes a topological space.

Attachment therapy

Attachment therapy (also called "the Evergreen model", "holding time", "rage-reduction", "compression therapy", "rebirthing", "corrective attachment therapy", and "coercive restraint therapy") is a pseudoscientific child mental health intervention intended to treat attachment disorders. It is found primarily in the United States, and much of it is centered in about a dozen clinics in Evergreen, Colorado, where Foster Cline, one of the founders, established his clinic in the 1970s.

Attachment in children

Attachment in children is "a biological instinct in which proximity to an attachment figure is sought when the child senses or perceives threat or discomfort. Attachment behaviour anticipates a response by the attachment figure which will remove threat or discomfort". Attachment also describes the function of availability, which is the degree to which the authoritative figure is responsive to the child's needs and shares communication with them.

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