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Metamath Proof Explorer

Theorem retps

Description: The standard topological space on the reals. (Contributed by NM, 19-Oct-2012)

		Ref	Expression
	Hypothesis	retps.k	$⊢ K = \{⟨{Base}_{ndx}, ℝ⟩, ⟨TopSet (ndx), topGen (ran (.))⟩\}$
	Assertion	retps	$⊢ K \in TopSp$

Step	Hyp	Ref	Expression
1		retps.k	$⊢ K = \{⟨{Base}_{ndx}, ℝ⟩, ⟨TopSet (ndx), topGen (ran (.))⟩\}$
2		uniretop	$⊢ ℝ = ⋃ topGen (ran (.))$
3		retop	$⊢ topGen (ran (.)) \in Top$
4	1 2 3	eltpsi	$⊢ K \in TopSp$