Thursday, July 14, 2011
Moksha is excited to present:
Connected & Disconnected Space
Illustrations by Jordan Kay
Opening Reception Friday ~ July 15 @ 8pm - 11pm
Cupcakes & Champagne
Exhibit runs through August 18th.
A space in which all components are one-point sets is called totally disconnected. Related to this property, a space X is called totally separated if, for any two elements x and y of X, there exist disjointed open neighborhoods. U of x and V of y such that X is the union of U and V. Clearly any totally separated space is totally disconnected, except the possibility of dark matter existing, therefore connecting all disconnected elements and spaces.
If there exists no two disjointed non-empty open sets in a space, X, X must be connected, and thus hyper-connected spaces are also connected. Since a simply connected space is, by definition, also required to be path connected, any simply connected space is also connected. Note however, that if the path connectedness requirement is dropped from the definition of simple connectivity, a simply connected space does not need to be connected. Yet stronger versions of connectivity include the notion of a contractible space. Every contractible space is path connected and thus also connected. Therefore in recent findings every space is theoretically connected.