Will the inverse mapping also be continuous? Suppose a map $f:A\to B$ is continuous and invertible. Will the inverse map $f^{-1}:B\to A$ be always continuous also?
Functions which are Continuous, but not Bicontinuous What are some examples of functions which are continuous, but whose inverse is not continuous?  nb: I changed the question after a few comments, so some of the below no longer make sense. Sorry.
How do I get the value of text input field using JavaScript? How do I install LibreOffice 4? I want to download and install .  How can I do this? How can I produce an encrypted Swap Partition for 14.04 ? All the advices I saw here are for versions &lt;14.04 and do not work for me.  I tried a lot but nothing lasted longer than a reboot.  On installation I decided to encrypt my home and 9 GiB partition for swap but this swap was never used by Kubuntu. Gparted finds an "unknown filesystem".  I many times formated it as swap, edited fstab and crypttab and used all the tricks mentioned in different answers here. The often mentioned PunyGeek letter does not work for me probably because /etc/initramfs-tools/conf.d/resume does not even exist on my system. 17.10 Super key to open applications Which command should I use for textual subscripts in math mode? Textual subscripts like in W_{total} should be typeset in an upright text font (so that code isn't good practice), as has been  in   . Now there are several ways to achieve this, and I'm somewhat confused which I should use:   W_{\rm total} is nice and short, and appears to work in all circumstances, but I expect LaTeX people will frown upon it :-) Is there any good reason against this? W_{\mathrm{total}} &ndash; is this the LaTeX equivalent of the \rm approach? W_{\textnormal{total}}  as total is text and not math&nbsp;... In , Ulrike Fischer suggests a more complicated approach. Even W_{\operatorname{total}} appears to work, but it seems inappropriate.   Note: I always assume here that amsmath is loaded.  I've already asked some questions above, but my main question is: which of these options is the best practice for textual subscripts?    Let me point out why I haven't mentioned \text, \textrm or \textup above. Those commands (mostly) keep the font of the context they're used in, e.g., in an italic context, \text and \textrm would give italic subscripts, and all three yield bold subscripts in a bold context.  Final note: This question is similar to, but not the same as all those  about the  between , , , ,  that have been asked before. Maybe it's still a duplicate&nbsp;... I've read the , and I don't get it. I am really interested, but I've read the explanation there a couple of times and I still don't get it how the Duff's device works.  What would a more detailed explanation be? Update values in one table based on contents of another Software Name: Oracle SQL Developer Version 17.2.0.188  I have three tables: orders, order_details, and products.  I wanted to run a query to update units_in_stock in the products table based on quantity in order_details, where the associated orders row has been marked as shipped, and has a shipping date.  Here's what I tried:  UPDATE Products SET (Products.Unit_In_Stock = Products.Unit_In_Stock - Order_Details.Quantity) INNER JOIN (     Orders INNER JOIN Order_Details ON Orders.Order_ID = Order_Details.Order_ID     ) ON Products.Product_ID = Order_Details.Product_ID WHERE (         ((Orders.Shipped_Date) IS NOT NULL)         AND ((Orders.This_Order_Was_Shipped) = "YES")         );   When I run this, I get:  Error at Command Line : 1 Column : 45   Line 1, Column 45 is the equal sign in the very first statement that said  Products.Unit_In_Stock = Products.Unit_In_Stock - Order_Details.Quantity   Can you help me get this working? I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong Show that if terms of a series have ratio less than the ratio of convergent series, then the series converges We have two infinite series $\sum a_n $ and $\sum b_n$, such that $a_n &gt; 0,\ b_n &gt; 0$ and $a_{n + 1}/a_n \leq b_{n + 1}/b_n$ for all $n$. Show that if $\sum b_n$ converges, then $\sum a_n$ also converges.   Any hints on how to prove this? I can sort of picture why this must be true, but I'm not sure how to prove this rigorously. I'm not sure using the ratio test would help here.. Difference between static class and singleton pattern? What real (i.e. practical) difference exists between a static class and a singleton pattern?  Both can be invoked without instantiation, both provide only one "Instance" and neither of them is thread-safe. Is there any other difference? How do I add newlines between lines printed on the command line? Mail logs are incredibly difficult to read. How could I output a blank line between each line printed on the command line? For example, say I'm grep-ing the log. That way, multiple wrapped lines aren't being confused. When water climbs up a piece of paper, where is the energy coming from? Take a glass of water and piece of toilet paper. If you keep the paper vertical, and touch the surface of the water with the tip of the paper, you can see the water being absorbed and climbing up the paper. This climbing up is intriguing me. Where is the energy coming from?  Supposedly, a lot of water molecules are moving up and gaining potential energy. This has to be balanced by something. I can think of a few possibilities, but I can't tell which one it is.   When the water molecules dilute into the paper, they are at a state of lower potential binding energy. Some molecular interaction (van der Waals?) is at lower energy when you have a water+paper solution, compared to a water-only solution. This compensates the gain in gravitational energy. The surface between the paper and the water is at lower pressure than the atmosphere. This causes the water to be pushed into the paper by the atmospheric pressure, up until the point that the column of water above the surface is heavy enough to counterbalance. The potential energy would be a result of work done by the atmosphere. Some water molecules climb up randomly and loose kinetic energy going up, and somehow get "stuck" up there. Something else? ToolStrip sometimes not responding to a mouse click Solve $\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt$ How to resolve the "GPT detected. Please create a BIOS-Boot partition" error when using boot-repair? After installing Ubuntu, Windows didn't boot so I installed boot repair to fix this problem. But I am getting the message displayed below.  I tried to make a new partition with unformatted file system but still receiving the same message.  How do I fix it? How to use `ybar interval` without skipping the last value Network button missing gone from Nautilus? I'm using Ubuntu 16.04.3 LTS.  I remember having a link in Nautilus that I used to browse network shares with in the past. I don't remember exactly but I think it was "Windows network" or "Browse network".  Now I can't find this on my current installation, there's only "Connect to server", but this is not what I want. Is there a way to put that link there? There is something strange going on with Books on iPad and iPhone. It keeps deleting some books locally, keeping them in the cloud.  It's frustrating because it happens when I'm offline and I simply lose the access to them.  Why is this happening at all? And how can I stop it?  I enabled syncing things over iCloud Drive and everything, but I can't see an option to disable such optimizations.    PS: the same thing happens with Photos, Numbers and Pages. The Photos app has an optimize storage option. But there doesn’t seem to be such an option for Books, Numbers and Pages.   A clear example: just a few hours I was reading a book on Books, I took a nap, and when I opened the Books app, the book was not available offline anymore. Since I don’t have internet right now, it’s simply impossible to access the document. Why my DAC works without GND and VCC? This is the most interesting thing I have seen! I have built a  that sends data (D0-D7) to a DAC (ADV2175). The design worked fine and I just have a low frequency alias noise (). This noise was present on all my ground planes (This is in prototyping stage and that's not unexpected from the test PCB).  I started tracing the noise path by disconnecting wires to see when the noise is gone. Surprisingly even after disconnecting all VCC and GND connections (+ all VREF and logics gone to 0 or 1) the noise was present yet. The more unexpected behavior is when the DAC is just connected to DATA port+ CLK pin (all coming from the source FPGA, NO VCC or GND), it continues working and a sine wave is produced (but with the same noise)!!!  First I thought it may receive its VCC/GND form the logic 1/0 fed into it but if it was correct, it should not have produce 0x00 and 0xFF levels, but it makes those levels correctly (I changed 0xFF data stage to another level and a notch appeared on top of the waves. this shows it can build oxFF correctly).    This is a big challenge for my PCB design, as if this device really takes its GND from the data port, instead of the dedicated pins, I will have a hard time for designing a reliable ground plane for it (the return voltage should go back to a logic noisy environment and analog-digital ground plane isolation may be impossible).  Can anyone explain what is happening there? points out that certain key and block lengths were a requirement for the AES submissions:     The candidate algorithm shall be capable of supporting key-block combinations with sizes of 128-128, 192-128, and 256-128 bits.   My question is this; how can having a key length that is greater than the block size enhance security?  If we look at ECB mode for simplicity, when the key length is equal to the block length we have a permutation relationship between the set of all plaintexts and the set of all ciphertexts.  Once you increase the key length beyond that, you start to introduce collisions. In fact, you only introduce collisions from then on don't you? Collisions in the sense that a key will create the same ciphertext-plantext relationship as another key.  This would lead me to believe that only part of the key-space is unique, and only that part of key-space needs to be brute-forced?  I know that I am clearly incorrect, I just don't understand why.