Some topology problems
#1
Đã gửi 01-05-2007 - 10:14
2. Let D be the decomposition of the plane into concentric circles about the origin. Prove that D is homeomorphic to {x R|x 0}.
3. Find a counterexample for:
"E X is disconnected iff there are disjoint open subsets H and K in X, each meeting E, such that E H K."
Thank you,
#2
Đã gửi 22-03-2017 - 19:35
1. Let ~ be the equivalence relation (x_{1}, x_{2}) ~ (y_{1}, y_{2}) iff x_{2}=y_{2}, on R^{2}. Then R^{2}/~ is homeomorphic to R.
2. Let D be the decomposition of the plane into concentric circles about the origin. Prove that D is homeomorphic to {x R|x 0}.
3. Find a counterexample for:
"E X is disconnected iff there are disjoint open subsets H and K in X, each meeting E, such that E H K."
Thank you,
$1)$ Easy , you can see that this equivalence just shrink or deformation of $R^{2}$ on $R$ where you connect all point to a line .
$2)$ Latexx
$3)$ By definition
Bài viết đã được chỉnh sửa nội dung bởi bangbang1412: 22-03-2017 - 19:38
- NTL2k1 yêu thích
$$[\Psi_f(\mathbb{1}_{X_{\eta}}) ] = \sum_{\varnothing \neq J} (-1)^{\left|J \right|-1} [\mathrm{M}_{X_{\sigma},c}^{\vee}(\widetilde{D}_J^{\circ} \times_k \mathbf{G}_{m,k}^{\left|J \right|-1})] \in K_0(\mathbf{SH}_{\mathfrak{M},ct}(X_{\sigma})).$$
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