Abhijeet Mulgund's Personal Webpage

Search

Search IconIcon to open search

Function Slice

Last updated Nov 1, 2022

# Definition

Let $X,Y,Z$ be Topological Spaces and suppose $F: X \times Y \to Z$ is a Function. Then the Function Slice of $F$ at $x \in X$ is the Function $y \mapsto F(x, y)$, denoted $F(x, \bullet)$ or $F_{x}$.

# Properties

  1. Slices of a Continuous Function are Continuous