Its is known every continuous function between topological spaces is sequentially continuous. Also sequentially continuity implies continuity if the domain space is first countable. I am interested in example of the function between topological spaces (where domain space is not first countable, as I say) that is sequentially continuous but not continuous.
Can you give me an example of a function which is sequentially continuous but not continuous? (I know that in first-countable spaces this is equivalent, but what about in spaces without this condition?)  Thank you :)
How to rate philosophy essays? I might end up teaching philosophy in Finnish lukio/gymnasium. I will not get an opportunity to practice teaching it - I do get to practice teaching mathematics a fair deal, though. (The situation is somewhat unfortunate.) I have taken subject studies in philosophy at university. They amount to around 60 credits (ECTS).  Suppose I give the students an exam, which asks them to write an essay or two. After that my task is to grade the exams in a fair way and comment them in such a way that the students can learn from the feedback.  -  Suppose the task was to write an essay on the problem of universals - nominalism and realism, say. Let us say 6 points is the perfect score for this task.  I would expect the students to define nominalism and realism (2 points, maybe?) and explain the problem (2 points). Remaining two points for taking some stance and arguing for it - realism is more reasonable because so and so. Partial credits for demonstrating only partial understanding.  -  Am I missing some important aspects of philosophical thinking? Should I emphasize the different parts of an answer in a different way? I suspect my perspective is influenced by fairly extensive mathematics education - is there something particular I should watch out for? Why does `last` show '{' and '|' in the TTY field? What is the term for accusing a person of mischief through invented, twisting and changeable terminology? What is the term for accusing a person of invented wrongdoing in such a way that he cannot respond or even clearly understand the accusations? For example, frequently reversing the definitions of the terminology used, or basing argumentation on hints and roundabout phrasings, metaphors, invented-on-the-fly floating definitions and rules to fit with the accusations.    Update: I think inquisitorial is the most proper term for context in which the result does not depend on the argumentation of one of the sides.    Though, jargonaut was completely unheard by me and incrementally more useful. I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but could not get satisfactory answer. Pleas help me understand it.  Here is the numerical, please consider it: A reversibe engine works between two temperatures whose difference is 100c. If it absorbs 746J of heat from the source and rejects 546J to the sink, calculate the temperature of the source and the sink. Ans (100°C, 0°C) Are there LaTeX performance profiling tools? Relativity and Galaxy Rotation Speed Command line option to check which filesystem I am using? Is there a command that will show which file system (ext3, ext4, FAT32, ...) the various partitions and disks are using?   Similar to how sudo fdisk -l lists information about disks and partitions? Why does (0 < 5 < 3) return true? How to use PostgreSQL/PostGIS with ArcGIS for Desktop? INT vs Unique-Identifier for ID field in database How is the minimum of a set of IID random variables distributed? If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general? What does var prime = num != 1; mean? What packages will let me use Cyrillic characters in math mode? Note I'm not actually planning on writing any, for instance, Russian prose or even any Russian words. It's just that, on paper, I've always had the habit of denoting sets by uppercase roman letters, sets of sets by script letters and, when the need arises, sets of sets of sets by uppercase Cyrillic letters. Is there some package I can load which will allow me to typeset (in LaTeX math mode) Cyrillic letters much as I would typeset Greek letters? ie. $\Zhe$ to produce an uppercase zhe. Thanks! Wolfram alpha says there are no solutions. Is this because of the following?  $$\tan(z)=i \Rightarrow \frac{e^{iz}-e^{-iz}}{i(e^{iz}+e^{-iz})}=i \Rightarrow \frac{e^{iz}-e^{-iz}}{(e^{iz}+e^{-iz})}=-1$$ Let $x=e^{iz}$. Then,  $$\frac{x-1/x}{x+1/x}=-1 \Rightarrow x-1/x=-x-1/x \Rightarrow 2x=0$$  Then, $$x=e^{iz} \Rightarrow \ln(0)=iz$$ but $\ln(0)$ does not exist so we have no solutions? elementary row operation change the eigenvalue of a matrix I'm having some difficulty with understanding why KVL (Kirchhoff voltage law) is valid when considering an AC circuit. I mean, the system is by definition not in steady state, right? That in turn means that the change in current causes a change in the magnetic field, which is manifested within the electric potential. I realize the potential is still defined and thus a line integral over a crossed curve of ALL of it's component should be zero.   However, what I often see (for, say, RLC circuits with an AC emf) is total disregard to the time varying components of the electric potential. Only the emf of the different components are considered and their sum is said to be zero. How can that be? What about the "second" part of the potentials? I already have a 6 month valid UK business visa received prior to April 24 2015. I was supposed to travel to the UK in April, but my trip was cancelled on medical grounds.  I am now planning to visit the UK in July for tourism. Would it be fine for me to do so? Will I be allowed to enter the UK? Should I carry the original invite letter and medical certificate to prove why I didn't go the first time? I would like to solve the beginner's standard exercise which claims that a point of $\mathrm{Spec} \ R$ is closed iff it is a maximal ideal.  The reverse implication is easy. The direct one seems much subtler. If $P = V(I)$ then, since there exist a maximal ideal $M$ containing $P$, it would follow that $\{P, M\} \subseteq V(I) = P$, whence $P=M$. In order to show the existence of $M$ I applied Zorn's lemma to the set of ideals containing $P$.  The question is the following: is there any other proof of the above implication that does not (indirectly) use the axiom of choice? My concern is that I may be using a cannon to shoot a fly. Also, it would be the first time that I see closedness of points to require the axiom of choice. If the axiom is indeed needed in general, are there "nice" classes of rings for which we could get away without it? Laplace equation of composite function Suppose we have $f(x,y)$, which satisfies Laplaces equation: $\frac{\delta^2f}{\delta x^2}+\frac{\delta^2f}{\delta y^2}=0$  Does $f(\frac{x}{x^2+y^2},\frac{y}{x^2+y^2})$ also satisfy Laplace equation? Is there any possibility to find my father's lost iPhone? My father has lost his iPhone 6 which was not signed in using an iCloud account. Is there any possibility it can be found?