countable base in Hindi - countable base meaning in Hindi

	1.	There exist ( necessarily non-compact ) topological surfaces having no countable base for their topology.
	2.	Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology.
	3.	;second-countable or "'perfectly separable "'if it has a countable base for its topology.
	4.	Accordingly, if the countable base consists entirely of finite elements, we obtain an order that is "'?-algebraic " '.
	5.	Thus, if one has a countable base for a topology then one has a countable local base at every point, and hence every second countable space is also a first-countable space.
	6.	Another surface having no countable base for its topology, but " not " requiring the Axiom of Choice to prove its existence, is the Pr�fer manifold, which can be described by simple equations that show it to be a real-analytic surface.
	7.	By contrast, the existence of the Pr�fer surface shows that there exist two-dimensional complex manifolds ( which are necessarily 4-dimensional real manifolds ) with no countable base . ( This is because any " n "-real-dimensional real-analytic manifold " Q " can be extended to an " n "-complex-dimensional complex manifold " W " that contains " Q " as a real-analytic submanifold .)

countable base meaning in Hindi