query: Topology generated by those subsets of $X$ which are preserved by images of nets in that subset by a function
positive_passages.docid: 24767
positive_passages.text: $N(X)$ denotes collection of all nets of $X$. $T:N(X)\to \mathcal{P}(X)$ be a map such that $T\{x_\delta\}=T\{y_\gamma\}$ if one is subnet of other.
negative_passages.docid: 70264
negative_passages.text: Prove that the inverse image of an open set is open
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 151358
negative_passages.text: Continuous image of a locally connected space which is not locally connected
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure
negative_passages.docid: 88595
negative_passages.text: Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
negative_passages.docid: 12490
negative_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: 17212
negative_passages.text: The preimage of a subset
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 28500
negative_passages.text: What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?
negative_passages.docid: 481
negative_passages.text: Can compact sets completey determine a topology?
negative_passages.docid: 21938
negative_passages.text: describing all possible topologies on a set
negative_passages.docid: 72190
negative_passages.text: Topological proof on discrete topology where $X$ is infinite
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 37654
negative_passages.text: Topology: Example of a compact set but its closure not compact
negative_passages.docid: 77563
negative_passages.text: Homeomorphism between spaces equipped with cofinite topologies
negative_passages.docid: 18828
negative_passages.text: Base and empty set of a topology