Simply Connected Space
In topology, a topological space is called simply connected (or 1-connected) if it is path-connected and every path between two points can be continuously transformed, staying within the space, into any other path while preserving the two endpoints in question (see below for an informal discussion).
If a space is not simply connected, it is convenient to measure the extent to which it fails to be simply connected; this is done by the fundamental group. Intuitively, the fundamental group measures how the holes behave on a space; if there are no holes, the fundamental group is trivial — equivalently, the space is simply connected.
Read more about Simply Connected Space: Informal Discussion, Formal Definition and Equivalent Formulations, Examples, Properties
Famous quotes containing the words simply, connected and/or space:
“You can’t write about people out of textbooks, and you can’t use jargon. You have to speak clearly and simply and purely in a language that a six-year-old child can understand; and yet have the meanings and the overtones of language, and the implications, that appeal to the highest intelligence.”
—Katherine Anne Porter (1890–1980)
“I like to see a home like this, a home connected with people’s thoughts and work, things they love.”
—Dewitt Bodeen (1908–1988)
“Mere human beings can’t afford to be fanatical about anything.... Not even about justice or loyalty. The fanatic for justice ends by murdering a million helpless people to clear a space for his law-courts. If we are to survive on this planet, there must be compromises.”
—Storm Jameson (1891–1986)