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A topological space is locally connected at the point x if every neighborhood of x contains a connected open neighborhood. It is called locally connected if it is locally ...

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, there exists a B_3 in S such that ...

The maximal irredundance polynomial R_G(x) for the graph G may be defined as the polynomial R_G(x)=sum_(k=ir(G))^(IR(G))r_kx^k, where ir(G) is the (lower) irredundance ...

The maximal matching-generating polynomial M_G(x) for the graph G may be defined as the polynomial M_G(x)=sum_(k=nu_L(G))^(nu(G))m_kx^k, where nu_L(G) is the lower matching ...

A topology induced by the metric g defined on a metric space X. The open sets are all subsets that can be realized as the unions of open balls B(x_0,r)={x in X|g(x_0,x)<r}, ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

A lattice which satisfies the identity (x ^ y) v (x ^ z)=x ^ (y v (x ^ z)) is said to be modular.