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Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.

X fulfils the T1-separation axiom and is regular. A space satisfying the T_3-separation axiom is said to be a T3-space.

A topological space fulfilling the T3-separation axiom: X fulfils the T1-separation axiom and is regular. According to the terminology of Alexandroff and Hopf (1972), ...

A topological space X fulfils the T1-separation axiom and is normal. A space fulfilling the T_4-separation axiom is said to be a T4-space.

A topological space fulfilling the T_4-axiom: X fulfils the T1-separation axiom and is normal. In the terminology of Alexandroff and Hopf (1972), T_4-space are called Tietze ...

When a Young tableau is constructed using the so-called insertion algorithm, an element starts in some position on the first row, from which it may later be bumped. In ...

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

The tail of a vector AB^-> is the initial point A, i.e., the point at which the vector originates. The tails of a statistical distribution with probability density function ...

A 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...