checking a string to be palindrome in root n time code example

Example: Write a function that tests whether a string is a palindrome

def palindrome_check(string):
    string = list(string)
    tmp = []
    #remove any spaces
    for x in range(0, len(string)):
        if(string[x] != " "):
            tmp.append(string[x].lower())
    
            
    #now reverse the string
    array1 = []
    i = 0
    j = len(tmp)-1

    while(i < len(tmp)):
        array1.append(tmp[j])
        i += 1
        j -= 1

    #check if array1 is equal to the string
    counter = 0
    for x in range(0, len(tmp)):
        if(tmp[x] == array1[x]):
            counter += 1

    #if the counter is equal to the length of the string then the word
    #is the same
    if(counter == len(tmp)):
        return True
    
    return False