query: Closure of image is subset of image of closure
positive_passages.docid: 12490
positive_passages.text: A map is continuous if and only if for every set, the image of closure is contained in the closure of image
negative_passages.docid: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 157330
negative_passages.text: Showing the image of a subgroup is a subgroup.
negative_passages.docid: 147914
negative_passages.text: Closed image of locally compact space
negative_passages.docid: 43248
negative_passages.text: Closure of a Ball is Contained in Closed Ball (usual metric)
negative_passages.docid: 117546
negative_passages.text: Idempotent of closure and other properties
negative_passages.docid: 107281
negative_passages.text: Proof of Existence of Algebraic Closure: Too simple to be true?
negative_passages.docid: 154474
negative_passages.text: Image of countable and uncountable sets
negative_passages.docid: 66895
negative_passages.text: A condition for the image of a metrizable space to be metrizable
negative_passages.docid: 116806
negative_passages.text: Find the weak sequential closure of a set in $L^2(-\pi,\pi)$
negative_passages.docid: 102048
negative_passages.text: Closure of a compact set in Regular space $ X $
negative_passages.docid: 158569
negative_passages.text: Proving a particular subset of $R^n$ is closed
negative_passages.docid: 21176
negative_passages.text: Closure of the set in dictionary order topology.
negative_passages.docid: 61930
negative_passages.text: Intersection of Closed and Compact Set is Closed
negative_passages.docid: 79697
negative_passages.text: If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
negative_passages.docid: 80546
negative_passages.text: Why is closure omitted in some group definitions?
negative_passages.docid: 23225
negative_passages.text: Union of connected subsets is connected if intersection is nonempty