Locally Connected Space

Locally Connected Space

In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.

Read more about Locally Connected Space:  Background, Definitions and First Examples, Properties, Components and Path Components, Quasicomponents, More On Local Connectedness Versus Weak Local Connectedness

Famous quotes containing the words locally, connected and/or space:

    To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.
    Clifford Geertz (b. 1926)

    As long as learning is connected with earning, as long as certain jobs can only be reached through exams, so long must we take this examination system seriously. If another ladder to employment was contrived, much so-called education would disappear, and no one would be a penny the stupider.
    —E.M. (Edward Morgan)

    Even the most subjected person has moments of rage and resentment so intense that they respond, they act against. There is an inner uprising that leads to rebellion, however short- lived. It may be only momentary but it takes place. That space within oneself where resistance is possible remains.
    bell hooks (b. c. 1955)