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 Mar 13 comment Pursuers (a game) @mvw The runner chooses arbitrary starting positions for both himself and for the pursuers. Mar 13 comment Pursuers (a game) @mvw The trajectory of the runner is any integral of an integrable vector function whose absolute value at every point is not above $v$. Likewise for pursuers (but with $u$ instead of $v$). If the runner's trajectory intersects one of a pursuer, the runner lose. Mar 11 comment Pursuers (a game) I don't know what is "round based". I ask whether initial positions, for which the runner may run infinitely, exist. In other words, initial positions can be taken arbitrarily. Initial velocity vectors are allowed to be arbitrary (as much that they are less $v$ for the runners and $u$ for the pursuers). Positions follow a differential equation for some continuous speed functions, that is are updated continuously. Mar 11 revised Pursuers (a game) added 71 characters in body; edited title Mar 11 asked Pursuers (a game) Feb 16 comment A totally bounded uniformity and certain filters @J.-E.Pin I think it is correct. However I asked this question almost a two years ago and may not remember the context of the issue. Feb 2 comment Circle is similar to a polygon with infinite number of sides @Kaster And I prefer it to be considered not as a limit, but as a "real" polygon with infinite number of sides. For example in complex number theory the infinity is not just a limit of finite values, but a quite particular point of Riemann sphere. Feb 2 comment Circle is similar to a polygon with infinite number of sides @Kaster I know that it is a limit. But what is the topology and what is the filter on which the limit is taken? Feb 2 asked Circle is similar to a polygon with infinite number of sides Jan 9 asked A property of product order Dec 17 awarded Yearling Nov 20 comment Name of the class of maps between posets such that $f(x)\le f(y)\implies x\le y$ Oh, if the implication holds also in the reverse direction, it is an order embedding. This is probably what I need Nov 19 revised Name of the class of maps between posets such that $f(x)\le f(y)\implies x\le y$ edited title Nov 19 asked Name of the class of maps between posets such that $f(x)\le f(y)\implies x\le y$ Oct 12 awarded Informed Oct 12 revised Embed boolean lattice into complete atomic boolean lattice added 40 characters in body Oct 12 asked Embed boolean lattice into complete atomic boolean lattice Oct 11 awarded Civic Duty Oct 11 accepted Intersection of two filters on a poset Oct 10 accepted Locally monotone function is monotone