2018-54.md

course	course_year	question_number	tags	title	year
Metric and Topological Spaces	IB	54	IB 2018 Metric and Topological Spaces	Paper 3, Section I, $3 E$	2018

What does it mean to say that a topological space is connected? If $X$ is a topological space and $x \in X$, show that there is a connected subspace $K_{x}$ of $X$ so that if $S$ is any other connected subspace containing $x$ then $S \subseteq K_{x}$.

Show that the sets $K_{x}$ partition $X$.