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Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6–8.The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum ...
It is locally connected if it has a base of connected sets. It can be shown that a space is locally connected if and only if every component of every open set of is open. Similarly, a topological space is said to be locally path-connected if it has a base of path-connected sets. An open subset of a locally path-connected space is connected if ...
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
Can each house be connected to each utility, with no connection lines crossing? Two views of the utility graph, also known as the Thomsen graph or K 3 , 3 {\displaystyle K_{3,3}} The classical mathematical puzzle known as the three utilities problem or sometimes water, gas and electricity asks for non-crossing connections to be drawn between ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
Similarly, a strict partial order that is connected is a strict total order. A relation is a total order if and only if it is both a partial order and strongly connected. A relation is a strict total order if, and only if, it is a strict partial order and just connected. A strict total order can never be strongly connected (except on an empty ...
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In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets.In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connected subsets.
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