Semilocal single connection

When a certain neighborhood U exists in mathematics particularly topology for any point x of topological space X, and the associate same model from the basic group of U led by inclusion map to the whole of X of U to the basic group of X becomes self-evident, it is said that it is a semilocal single connection in X (はんきょくしょたんれんけつ British: semi-locally simply connected).

The Hawaiian earring is not a semilocal single connection

The space that is a local single connection is a semilocal single connection obviously as well as the space that is a single connection. An example of the space that is not a semilocal single connection includes Hawaiian earring (British: Hawaiian earring). This is sum of sets of Japanese yen of central (1/n, 0) radius 1/n on Euclid plane for a positive integer n. Then any near origin includes Japanese yen that is not ホモトープ in 0.

The semilocal single connectibility is weaker than local single connectibility. I think about the cone on the Hawaiian earring to see this. This is the semitherefore local single connection that is a possible shrinkage (British: contractible), but is not a clearly local single connection.

When a certain space is an arc connection, a local arc connection and a semilocal single connection and, by the coating space idea, is known to have universality coating only for that case.

It is acquired by "https://ja.wikipedia.org/w/index.php?title= half local site single connection &oldid=62632594"

This article is taken from the Japanese Wikipedia Semilocal single connection

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