Category:Quotient Topology
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This category contains results about the quotient topology.
Definitions specific to this category can be found in Definitions/Quotient Topology.
Let $T = \struct {S, \tau}$ be a topological space.
Let $\RR \subseteq S \times S$ be an equivalence relation on $S$.
Let $q_\RR: S \to S / \RR$ be the quotient mapping induced by $\RR$.
Definition 1
Let $\tau_\RR$ be the identification topology on $S / \RR$ by $q_\RR$:
- $\tau_\RR := \set {U \subseteq S / \RR: q_\RR^{-1} \sqbrk U \in \tau}$
Then $\tau_\RR$ is the quotient topology on $S / \RR$ by $q_\RR$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Q
- Quotient Spaces (15 P)
Pages in category "Quotient Topology"
The following 10 pages are in this category, out of 10 total.
C
I
Q
- Quotient Mapping and Continuous Mapping Induces Continuous Mapping
- Quotient Mapping and Continuous Mapping Induces Continuous Mapping/Corollary
- Quotient Mapping equals Surjective Identification Mapping
- Quotient Mapping Induces Homeomorphism between Quotient Space and Image
- Quotient Topology is Topology