first-countable space oor Spaans
first-countable space
Vertalings in die woordeboek Engels - Spaans
Primer axioma de numerabilidad
en
topological space satisfying the "first axiom of countability"
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However, the approach to convergence in a topological space using sequences is sufficient when the space satisfies the first axiom of countability (as metrizable spaces do), but generally not otherwise.
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This space is Hausdorff, paracompact and first countable.
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However, the product of uncountably many metrizable spaces, each with at least two points, fails to be first countable.
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When viewed as a topological space, ω1 is often written as = ω1 + 1 is compact and not first-countable. ω1 is used to define the long line and the Tychonoff plank, two important counterexamples in topology.
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A subset A of a topological space X is closed in X if and only if every limit of every net of elements of A also belongs to A. In a first-countable space (such as a metric space), it is enough to consider only convergent sequences, instead of all nets.
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Metrizable spaces are always Hausdorff and paracompact (and hence normal and Tychonoff), and first-countable.
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If X is a space and A is a subset of X, then A is meagre in X (or of first category in X) if it is the countable union of nowhere dense sets.
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7 sinne gevind in 10 ms. Hulle kom uit baie bronne en word nie nagegaan nie.