<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Questions tagged [topological-groups]

      A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

      Filter by
      Sorted by
      Tagged with
      1
      vote
      1answer
      53 views

      Structure of extensions arising in Lie approximation of connected groups

      My imperfect understanding is that, by the work of various authors (Gleason, Yamabe, Montgomery, Zippin ...), the following result is known: Let $G$ be a connected, locally compact, Hausdorff group, ...
      3
      votes
      0answers
      46 views

      Are $T_0$ topological quasigroups completely regular?

      In 1957 H. Salzmann generalized to quasigroups but weakened the standard result that $T_0$ topological groups are completely regular. He was able to show that $T_0$ topological quasigroups are regular ...
      10
      votes
      1answer
      160 views

      The rigidity of the countable product of free groups

      For a natural number $n$ let $F_n$ be the free group with $n$ generators. The group $F_n$ is endowed with the discrete topology. Given an increasing sequence $\vec p=(p_k)_{k\in\omega}$ of prime ...
      4
      votes
      0answers
      52 views

      Invariant measure on coset space and integrable functions

      Let $G$ be a locally compact abelian group, and $H$ a closed subgroup. Let $C_c(G)$ be the space of continuous, compactly supported complex valued functions on $G$. General theory of Haar measure ...
      2
      votes
      1answer
      149 views

      How to prove that Chevalley groups over $\mathbb R$ have no compact factors

      I am trying to see why the Chevalley groups (not limited to the adjoint group) over $\mathbb R$ are without compact factors in order to use the Borel density theorem. I've been told in another thread ...
      1
      vote
      0answers
      131 views

      Describing compact Lie groups in purely topological terms

      Compact Lie groups are a very special type of compact group, namely those which admit a differentiable structure. Is it possible to describe compact Lie groups in purely topological terms, that is, ...
      4
      votes
      0answers
      142 views

      Polish groups with no small subgroups

      Definitions. A Polish group is a topological group $G$ that is homeomorphic to a separable complete metric space. A group $G$ has no small subgroups if there exists a neighborhood $U$ of the identity ...
      3
      votes
      0answers
      99 views

      Topological derivation of the Laplace formula for determinants in Euclidean space

      I'm interested in trying to derive the Leibniz formula for the determinant on real Euclidean space, without first constructing $\det$ by axiomatizing its properties. We know $GL(n)$ deformation ...
      3
      votes
      1answer
      104 views

      Reduction of the structure group of $\mathbb{R}^n$-fiber bundles to a special subgroup of $\mathrm{Homeo}(\mathbb{R}^n)$

      Let $G$ be the group of all self-homeomorphisms $f$ of $\mathbb{R}^n$ which satisfy $$f(x+m)=f(x)+m,\quad \forall m\in \mathbb{Z}^n.$$ In other words, $G$ is the group of all equivariant self-...
      1
      vote
      1answer
      66 views

      When are function groups monothetic?

      Let us consider the group of continuous functions $C(S^1, S^1)$ from the circle to itself with the compact open topology. Does it have a chance to contain a dense cyclic subgroup? Unfortunately it ...
      6
      votes
      0answers
      41 views

      Special monomorphism to encode the inclusion of topological submonoids

      Consider the category $\mathrm{TopMon}$ of topological monoids and continuous monoid homomorphisms. Consider the inclusion $i:\Bbb{R}_{\ge 0}\hookrightarrow \Bbb{R}$, where the spaces are taken with ...
      2
      votes
      0answers
      44 views

      Factorization of characters

      Linked to the end of this question here and because the subject involves many deformations of shuffle, I came to the following Let $k$ be a $\mathbb{Q}$-algebra and $\mathfrak{g}$ a $k$-Lie algebra, ...
      1
      vote
      0answers
      182 views

      Trying to understand an argument to put a topology on $GL_n(R)$ when $R$ is a topological ring

      I'm reading this set of notes and I'm trying to understand this passage where they explain how to put a topology on $GL_n(R)$ when $R$ is a topological ring, which I am not completely following. The ...
      6
      votes
      0answers
      126 views

      Short exact sequence of free topological groups

      Suppose that $K\rightarrow G \rightarrow G/K $ is a short exact sequence of topological groups such that $G$ and $G/K$ are free topological groups. Is it true that we have a continuous section $s: G/K\...
      3
      votes
      1answer
      226 views

      Is the ring of $p$-adic integers extremally disconnected?

      We call a topological space $X$ extremally disconnected if the closures of its open sets remain open. Obviously, Hausdorff extremally disconnected spaces are totally disconnected in the sense that ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>

              老11选5开奖视频 黑龙江时时软件 四川时时号码查询结果 河北排列七中奖多少钱 七乐彩期走势图带连线 沙巴体育外围 快乐12辽宁开奖结果走势图 凤凰平台时时彩奖金 上海时时开奖纪录 四川时时12选5结果走势图