sequential space

He used the 10 digits of our decimal system to specify individual words by sequential space and number.

There are sequential spaces that are not first countable.

A sequential space is a space X satisfying one of the following equivalent conditions:

Every sequential space is also a Pytkeev space.

Thus every premetric space is a topological space, and in fact a sequential space.

Every sequential space (in particular, every metrizable space) is countably generated.

There is also a notion of a Fréchet-Urysohn space as a type of sequential space.

Sequential spaces are the most general class of spaces for which sequences suffice to determine the topology.

Every sequential space has countable tightness.

The full subcategory Seq of all sequential spaces is closed under the following operations in Top:

In a sequential space sequential compactness is equivalent to countable compactness.

A space is a Fréchet-Urysohn space if and only if every subspace is a sequential space.

In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability.

These clever spaces set up a dialogue between the old fashioned sequential spaces of the Museum and the in-process spaces of Kunsthalle.

The final equivalent condition shows that the class of sequential spaces consists precisely of those spaces whose topological structure is determined by convergent sequences in the space.

Since they are closed under topological sums and quotients, the sequential spaces form a coreflective subcategory of the category of topological spaces.

A parallel machine must be sufficiently powerful to emulate the sequential machine in time polynomially related to the sequential space; compare Turing machine, non-deterministic Turing machine, and alternating Turing machine.

Given a topology with respect to which the sequential closure operator is defined, the topological space is a sequential space if and only if the topology generated by is equal to , that is, if .

The game consists of a wooden case with a dragonfly motif, a board with sequential spaces laid out in a spiral, an instruction sheet, small wooden playing pieces, two dice, a set of cards, and a central tower with two snakes and a dial.

In mathematics, a topological space X is called countably generated if the topology of X is determined by the countable sets in a similar way as the topology of a sequential space (or a Fréchet space) by the convergent sequences.